**INSTANT DOWNLOAD COMPLETE TEST BANK WITH ANSWERS**** ****Quantitative Analysis for Management 11th Edition by Barry Render – Test Bank**** ****Sample Questions** *Quantitative Analysis for Management, 11e*** (Render)****Chapter 6 Inventory Control Models**** **1) Inventory is such an expensive asset that it may account for as much as 50 percent of a firm’s invested capital.Answer: TRUEDiff: 2Topic: INTRODUCTION 2) The same ratio of marginal loss to the sum of marginal loss and marginal profit is used to solve one-period inventory models for both discrete and continuous probability distributions.Answer: TRUEDiff: 3Topic: SINGLE-PERIOD INVENTORY MODELS 3) In the decoupling function, some inventory may be stored between each production process to act as a buffer.Answer: TRUEDiff: 2Topic: IMPORTANCE OF INVENTORY CONTROL 4) Service level is the chance, measured in percent, that there will be a stockout.Answer: FALSEDiff: 2Topic: USE OF SAFETY STOCK 5) A stockout is a situation that occurs when there is no inventory on hand.Answer: TRUEDiff: 1Topic: INTRODUCTION 6) The concept of inventory is applicable to both manufacturing and service organizations.Answer: TRUEDiff: 1Topic: INTRODUCTION 7) One reason inventory is required is the uneven flow of resources through a company.Answer: TRUEDiff: 2Topic: IMPORTANCE OF INVENTORY CONTROL 8) Inventory is any stored resource that is used to satisfy a current or future need.Answer: TRUEDiff: 1Topic: INTRODUCTION 9) Economic order quantity (EOQ) analysis has recently become practical as a consequence of high-speed computers.Answer: FALSEDiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDER10) Inventory is the common thread that ties all the functions and departments of the organization together.Answer: TRUEDiff: 2Topic: INTRODUCTION 11) The purpose of the EOQ model is to achieve a balance between the cost of holding inventory and the cost of stockouts.Answer: FALSEDiff: 1Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDER 12) Under the assumptions made to develop the EOQ model, average inventory is one-half of the maximum inventory.Answer: TRUEDiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDER 13) The EOQ model is relatively insensitive to minor violations of the basic assumptions.Answer: TRUEDiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDER 14) The production run model is useful when a firm purchases inventory that is delivered over a period of time.Answer: TRUEDiff: 2Topic: EOQ WITHOUT THE INSTANTANEOUS RECEIPT ASSUMPTION 15) The two fundamental decisions that you have to make when controlling inventory are: (1) how much to order, and (2) how much money to spend.Answer: FALSEDiff: 2Topic: INVENTORY DECISIONS 16) The economic order quantity helps one estimate the optimal number of units to purchase with each order.Answer: TRUEDiff: 1Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDER 17) The reorder point occurs during a stockout.Answer: FALSEDiff: 2Topic: REORDER POINT: DETERMINING WHEN TO ORDER 18) Safety stock is ignored when computing the reorder point.Answer: FALSEDiff: 2Topic: USE OF SAFETY STOCK19) In a quantity discount model, the purchase cost or material cost must be included in the total cost calculation.Answer: TRUEDiff: 2Topic: QUANTITY DISCOUNT MODELS 20) Theft is one of the “ordering cost factors.”Answer: FALSEDiff: 2Topic: INVENTORY DECISIONS 21) Purchasing department supplies comprise one of the “carrying cost factors.”Answer: FALSEDiff: 2Topic: INVENTORY DECISIONS 22) We can usually determine an appropriate safety stock even if we are unable to accurately assess the actual cost of a stockout.Answer: TRUEDiff: 1Topic: USE OF SAFETY STOCK 23) One of the assumptions of the basic EOQ model is that the receipt of inventory is instantaneous.Answer: TRUEDiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDER 24) ABC analysis places inventory into 26 categories for computer analysis.Answer: FALSEDiff: 1Topic: ABC ANALYSIS 25) In ABC inventory analysis, items in the “A” group should have the lowest dollar value to the firm.Answer: FALSEDiff: 2Topic: ABC ANALYSIS 26) The costs involved in a typical inventory model are order costs, management costs, and holding costs.Answer: FALSEDiff: 2Topic: INVENTORY DECISIONS 27) ERP systems are expensive to buy and costly to customize.Answer: TRUEDiff: 2Topic: ENTERPRISE RESOURCE PLANNING28) Inventory

- A) is any stored resource used to satisfy current or future need.
- B) includes raw materials, work-in-process, and finished goods.
- C) levels for finished goods are a direct function of demand.
- D) needs from raw materials through finished goods can be reasonably determined, once finished goods demand is determined.
- E) All of the above

Answer: EDiff: 1Topic: INTRODUCTION 29) Which of the following is __not__ a use of inventory?

- A) the decoupling function
- B) quantity discounts
- C) irregular supply and demand
- D) the translucent function
- E) to avoid stockouts and shortages

Answer: DDiff: 1Topic: IMPORTANCE OF INVENTORY CONTROL 30) In making inventory decisions, the purpose of the basic EOQ model is to

- A) minimize carrying costs.
- B) minimize ordering costs.
- C) minimize the sum of carrying costs and ordering costs.
- D) minimize customer dissatisfaction.
- E) minimize stock on hand.

Answer: CDiff: 2Topic: INVENTORY DECISIONS 31) Which of the following is __not__ considered a significant inventory cost?

- A) cost of production labor
- B) purchase cost
- C) cost of stockouts
- D) cost of carrying an item
- E) cost of ordering

Answer: ADiff: 2Topic: INVENTORY DECISIONS 32) Which of the following is part of the determination of EOQ?

- A) cost of production labor
- B) cost of stockouts
- C) purchase cost
- D) annual demand
- E) total revenue

Answer: DDiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDER33) Which of the following factors is (are) __not__ included in ordering cost?

- A) bill paying
- B) obsolescence
- C) purchasing department overhead costs
- D) inspecting incoming inventory
- E) developing and sending purchase orders

Answer: BDiff: 2Topic: INVENTORY DECISIONS 34) Which of the following factors is (are) __not__ included in carrying cost?

- A) spoilage
- B) obsolescence
- C) cost of capital
- D) inspecting incoming inventory
- E) warehousing overhead costs

Answer: DDiff: 2Topic: INVENTORY DECISIONS 35) Mark Achin sells 3,600 electric motors each year. The cost of these is $200 each, and demand is constant throughout the year. The cost of placing an order is $40, while the holding cost is $20 per unit per year. There are 360 working days per year and the lead-time is 5 days. If Mark orders 200 units each time he places an order, what would his total ordering cost be for the year?

- A) $2,000
- B) $2,720
- C) $200
- D) $720
- E) None of the above

Answer: DDiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDERAACSB: Analytic Skills 36) The annual demand for a product has been projected at 2,000 units. This demand is assumed to be constant throughout the year. The ordering cost is $20 per order, and the holding cost is 20 percent of the purchase cost. The purchase cost is $40 per unit. There are 250 working days per year. Currently, the company is ordering 500 units each time an order is placed. Assuming the company uses a safety stock of 20 units resulting in a reorder point of 60 units, what is the expected lead-time for delivery?

- A) 4 days
- B) 5 days
- C) 6 days
- D) 7 days
- E) None of the above

Answer: BDiff: 3Topic: USE OF SAFETY STOCKAACSB: Analytic Skills 37) The objective of a(n) ________ system is to reduce costs by integrating all of the operations of a firm.

- A) MRP
- B) ERP
- C) JIT
- D) VMI
- E) EOQ

Answer: BDiff: 2Topic: ENTERPRISE RESOURCE PLANNING 38) As the service level increases,

- A) carrying cost increases at an increasing rate.
- B) carrying cost increases at a decreasing rate.
- C) carrying cost decreases at a decreasing rate.
- D) carrying cost decreases at an increasing rate.
- E) None of the above

Answer: ADiff: 2Topic: USE OF SAFETY STOCK 39) R. C. Barker makes purchasing decisions for his company. One product that he buys costs $50 per unit when the order quantity is less than 500. When the quantity ordered is 500 or more, the price per unit drops to $48. The ordering cost is $30 per order and the annual demand is 7,500 units. The holding cost is 10 percent of the purchase cost. If R. C. orders 500 units each time he places an order, what would the total annual holding cost be?

- A) $450
- B) $1,200
- C) $1,250
- D) $2,400
- E) None of the above

Answer: BDiff: 2Topic: QUANTITY DISCOUNT MODELSAACSB: Analytic Skills 40) Which of the following is __not__ an assumption for the basic EOQ model?

- A) Only an integer number of orders can be made each year.
- B) Quantity discounts are not possible.
- C) Inventory receipt is instantaneous (all at once).
- D) With orders placed at the correct time, there will be no shortages.
- E) Demand is known.

Answer: ADiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDER 41) For the basic EOQ model, which of the following relationships is __not__ true?

- A) The optimal number of orders per year equals annual demand divided by the EOQ.
- B) The reorder point equals daily demand multiplied by the lead-time in days, excluding safety stock.
- C) Average inventory level equals one-half the order size.
- D) The average dollar level of inventory equals unit price multiplied by order quantity.
- E) At EOQ, annual ordering cost equals annual carrying cost.

Answer: DDiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDER 42) The EOQ model without the instantaneous receipt assumption is commonly called the

- A) quantity discount model.
- B) safety stock model.
- C) planned shortage model.
- D) production run model.
- E) None of the above

Answer: DDiff: 2Topic: EOQ WITHOUT THE INSTANTANEOUS RECEIPT ASSUMPTION 43) Which of the following is __not__ a potential drawback of an ERP system?

- A) Training employees on the use of the new software can be expensive.
- B) The software is costly to customize.
- C) The software is expensive to buy.
- D) The implementation may require a company to change its normal operations.
- E) It does not incorporate inventory control decisions.

Answer: EDiff: 1Topic: ENTERPRISE RESOURCE PLANNING 44) Sensitivity analysis of EOQ refers to

- A) the attitude of top management toward the use of the EOQ model.
- B) analysis of how much the EOQ will change if different input values are used.
- C) an assessment of the impact of obsolescence upon the EOQ.
- D) a study of the impact of storing incompatible products in the same warehouse.
- E) analysis of the impact of stock shortages on customers or on production.

Answer: BDiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDER 45) Which of the following is __not__ a benefit of a well-developed ERP system?

- A) It is relatively inexpensive to customize.
- B) It can integrate all of the operations of a firm.
- C) It can reduce transaction costs.
- D) It can increase speed of information.
- E) It can increase accuracy of information.

Answer: ADiff: 2Topic: ENTERPRISE RESOURCE PLANNING46) The annual demand for a product has been projected at 2,000 units. This demand is assumed to be constant throughout the year. The ordering cost is $20 per order, and the holding cost is 20 percent of the purchase cost. Currently, the purchase cost is $40 per unit. There are 250 working days per year. Whenever an order is placed, it is known that the entire order will arrive on a truck in 6 days. Currently, the company is ordering 500 units each time an order is placed. What is the total holding cost for the year using this policy?

- A) $400
- B) $2,000
- C) $4,000
- D) $8,000
- E) None of the above

Answer: BDiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDERAACSB: Analytic Skills 47) Mark Achin sells 3,600 electric motors each year. The cost of these is $200 each, and demand is constant throughout the year. The cost of placing an order is $40, while the holding cost is $20 per unit per year. There are 360 working days per year and the lead-time is 5 days. If Mark orders 200 units each time he places an order, what would his average inventory be (in units)?

- A) 100
- B) 200
- C) 60
- D) 120
- E) None of the above

Answer: ADiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDERAACSB: Analytic Skills 48) Andre Candess manages an office supply store. One product in the store is computer paper. Andre knows that 10,000 boxes will be sold this year at a constant rate throughout the year. There are 250 working days per year and the lead-time is 3 days. The cost of placing an order is $30, while the holding cost is $15 per box per year. How many units should Andre order each time?

- A) 200
- B) 400
- C) 500
- D) 100
- E) None of the above

Answer: ADiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDERAACSB: Analytic Skills 49) Daniel Trumpe has computed the EOQ for a product he sells to be 400 units. However, due to recent events he has a cash flow problem. Therefore, he orders only 100 units each time he places an order. Which of the following is true for this situation?

- A) Annual ordering cost will be lower than annual holding cost.
- B) Annual ordering cost will be higher than annual holding cost.
- C) Annual ordering cost will equal annual holding cost.
- D) Annual ordering cost will be unaffected by the order policy change.
- E) Nothing can be determined without more information.

Answer: BDiff: 3Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDERAACSB: Reflective Thinking 50) With ________, inventory arrives just before it is needed.

- A) VMI
- B) ABC
- C) ERP
- D) JIT
- E) JBT

Answer: DDiff: 1Topic: JUST-IN-TIME INVENTORY CONTROL 51) In a JIT system, inventory managers can uncover bottlenecks by introducing or removing which of the following?

- A) C-kanbans
- B) P-kanbans
- C) E-kanbans
- D) T-kanbans
- E) I-kanbans

Answer: BDiff: 2Topic: JUST-IN-TIME INVENTORY CONTROL 52) Which of the following does __not__ have an impact on EOQ?

- A) safety stock
- B) demand per unit time
- C) order cost
- D) holding cost
- E) None of the above

Answer: ADiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDER and USE OF SAFETY STOCK 53) The demand during the lead-time is normally distributed with a mean of 40 and a standard deviation of 4. If they have calculated a reorder point of 46.60 units, what service level are they assuming?

- A) 85 percent
- B) 90 percent
- C) 95 percent
- D) 97.5 percent
- E) None of the above

Answer: CDiff: 3Topic: USE OF SAFETY STOCKAACSB: Analytic Skills 54) Judith Thompson is the manager of the student center cafeteria. She is introducing pizza as a menu item. The pizza is ordered frozen from a local pizza establishment and baked at the cafeteria. Judith anticipates a weekly demand of 10 pizzas. The cafeteria is open 45 weeks a year, 5 days a week. The ordering cost is $15 and the holding cost is $0.40 per pizza per year. What is the optimal number of pizzas Judith should order?

- A) 184 pizzas
- B) 9 pizzas
- C) 5 pizzas
- D) 28 pizzas
- E) None of the above

Answer: ADiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDERAACSB: Analytic Skills 55) What shows how many units are needed at every level of production?

- A) production level tree
- B) material requirements tree
- C) decision tree
- D) material structure tree
- E) Christmas tree

Answer: DDiff: 2Topic: DEPENDENT DEMAND: THE CASE FOR MATERIAL REQUIREMENTS PLANNING 56) R. C. Barker makes purchasing decisions for his company. One product that he buys costs $50 per unit when the order quantity is less than 500. When the quantity ordered is 500 or more, the price per unit drops to $48. The ordering cost is $30 per order and the annual demand is 7,500 units. The holding cost is 10 percent of the purchase cost. If R. C. wishes to minimize his total annual inventory costs, he must evaluate the total cost for two possible order quantities. What are these two possible quantities? (Round answer to nearest unit.)

- A) 300 and 306
- B) 300 and 500
- C) 306 and 50
- D) 200 and 306
- E) None of the above

Answer: BDiff: 2Topic: QUANTITY DISCOUNT MODELSAACSB: Analytic Skills57) The annual demand for a product is 1,000 units. The company orders 200 units each time an order is placed. The lead-time is 6 days, and the company has determined that 20 units should be held as a safety stock. There are 250 working days per year. What is the reorder point?

- A) 20
- B) 24
- C) 44
- D) 120
- E) None of the above

Answer: CDiff: 2Topic: USE OF SAFETY STOCKAACSB: Analytic Skills 58) The annual demand for a product has been projected at 2,000 units. This demand is assumed to be constant throughout the year. The ordering cost is $20 per order, and the holding cost is 20 percent of the purchase cost. Currently, the purchase cost is $40 per unit. There are 250 working days per year. Whenever an order is placed, it is known that the entire order will arrive on a truck in 6 days. Currently, the company is ordering 500 units each time an order is placed. What should be the reorder point (excluding any safety stock) under the current policy?

- A) 48
- B) 100
- C) 6
- D) 24
- E) None of the above

Answer: ADiff: 2Topic: REORDER POINT: DETERMINING WHEN TO ORDERAACSB: Analytic Skills 59) Andre Candess manages an office supply store. One product in the store is computer paper. Andre knows that 10,000 boxes will be sold this year at a constant rate throughout the year. There are 250 working days per year and the lead-time is 3 days. The cost of placing an order is $30, while the holding cost is $15 per box per year. If Andre orders 500 boxes each time he orders from his supplier, what would his total annual inventory cost be (holding cost plus ordering cost)?

- A) $3,000
- B) $4,350
- C) $3,075
- D) $3,750
- E) None of the above

Answer: BDiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDERAACSB: Analytic Skills 60) Rolf Steps is the production manager for a local manufacturing firm. This company produces staplers and other items. The holding cost is $2 per unit per year. The cost of setting up the production line for this is $25. There are 200 working days per year. The production rate for this product is 80 per day. If the production order quantity is 200 units, what was the daily demand (rounded to the nearest whole unit)?

- A) 6 units
- B) 7 units
- C) 8 units
- D) 9 units
- E) None of the above

Answer: BDiff: 3Topic: EOQ WITHOUT THE INSTANTANEOUS RECEIPT ASSUMPTIONAACSB: Analytic Skills 61) The “point at which to reorder” depends directly on which of the following?

- A) EOQ
- B) ordering cost
- C) lead-time
- D) storage costs
- E) unit purchasing cost

Answer: CDiff: 2Topic: REORDER POINT: DETERMINING WHEN TO ORDERAACSB: Analytic Skills 62) Judith Thompson, the manager of the student center cafeteria, has added pizza to the menu. The pizza is ordered frozen from a local pizza establishment and baked at the cafeteria. Judith anticipates a weekly demand of 10 pizzas. The cafeteria is open 45 weeks a year, 5 days a week. The ordering cost if $15 and the holding cost is $0.40 per pizza per year. The pizza vendor has a 4-day lead-time and Judith wants to maintain 1 pizza for safety stock. What is the optimal reorder point?

- A) 10
- B) 8
- C) 4
- D) 9
- E) None of the above

Answer: DDiff: 2Topic: USE OF SAFETY STOCKAACSB: Analytic Skills 63) R. C. Barker makes purchasing decisions for his company. One product that he buys costs $50 per unit when the order quantity is less than 500. When the quantity ordered is 500 or more, the price per unit drops to $48. The ordering cost is $30 per order and the annual demand is 7,500 units. The holding cost is 10 percent of the purchase cost. How many units should R. C. order to minimize his total annual inventory cost? (Round your answer to the nearest unit.)

- A) 300
- B) 306
- C) 500
- D) 200
- E) None of the above

Answer: CDiff: 3Topic: QUANTITY DISCOUNT MODELSAACSB: Analytic Skills 64) The annual demand for a product has been projected at 2,000 units. This demand is assumed to be constant throughout the year. The ordering cost is $20 per order, and the holding cost is 20 percent of the purchase cost. Currently, the purchase cost is $40 per unit. There are 250 working days per year. Whenever an order is placed, it is known that the entire order will arrive on a truck in 6 days. How many units should the company order each time an order is placed if the company wishes to minimize total inventory cost?

- A) 100
- B) 200
- C) 250
- D) 500
- E) None of the above

Answer: ADiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDERAACSB: Analytic Skills 65) Consider the material structure tree for item A below. If 20 units of A are needed, how many units of D are needed?

- A) 11
- B) 30
- C) 160
- D) 60
- E) 220

Answer: EDiff: 2Topic: DEPENDENT DEMAND: THE CASE FOR MATERIAL REQUIREMENTS PLANNINGAACSB: Analytic Skills 66) Consider the material structure tree for item A below. If 10 units of A are needed, how many units of E are needed?

- A) 60
- B) 6
- C) 240
- D) 24
- E) 480

Answer: CDiff: 2Topic: DEPENDENT DEMAND: THE CASE FOR MATERIAL REQUIREMENTS PLANNINGAACSB: Analytic Skills 67) Extra inventory that is used to avoid stockouts is known as

- A) planned shortages.
- B) quantity discounts.
- C) safety stock.
- D) service level.
- E) ABC analysis.

Answer: CDiff: 1Topic: USE OF SAFETY STOCK 68) An inventory model that can handle dependent demand is called a(n)

- A) MRP system.
- B) JIT system.
- C) ERP system.
- D) Kanban system.
- E) VMI system.

Answer: ADiff: 1Topic: DEPENDENT DEMAND: THE CASE FOR MATERIAL REQUIREMENTS PLANNING 69) As the service level increases,

- A) safety stock increases at a decreasing rate.
- B) safety stock increases at an increasing rate.
- C) safety stock decreases at an increasing rate.
- D) safety stock decreases at a decreasing rate.
- E) None of the above

Answer: BDiff: 2Topic: USE OF SAFETY STOCK 70) A person is using the normal distribution to determine the safety stock for a product. What z value would be associated with a 90 percent service level?

- A) 0.90
- B) 1.28
- C) 0.53
- D) 0.90
- E) None of the above

Answer: BDiff: 2Topic: USE OF SAFETY STOCK 71) The demand during the lead-time is normally distributed with a mean of 40 and a standard deviation of 4. If the company wishes to maintain a 90 percent service level, how much safety stock should be held?

- A) 45.12
- B) 41.28
- C) 1.28
- D) 5.12
- E) None of the above

Answer: DDiff: 2Topic: USE OF SAFETY STOCK 72) The annual demand for a product is 1,000 units. The company orders 200 units each time an order is placed. The lead-time is 6 days. There are 250 working days per year. If the reorder point is 50, what safety stock are they using?

- A) 22
- B) 4
- C) 26
- D) 28
- E) None of the above

Answer: CDiff: 3Topic: USE OF SAFETY STOCKAACSB: Analytic Skills 73) The annual demand for a product has been projected at 2,000 units. This demand is assumed to be constant throughout the year. The ordering cost is $20 per order, and the holding cost is 20 percent of the purchase cost. The purchase cost is $40 per unit. There are 250 working days per year. Whenever an order is placed, it is known that the entire order will arrive on a truck in 6 days. Currently, the company is ordering 500 units each time an order is placed. What level of safety stock would give a reorder point of 60 units?

- A) 10
- B) 14
- C) 18
- D) 12
- E) 22

Answer: DDiff: 3Topic: USE OF SAFETY STOCKAACSB: Analytic Skills 74) A person is using the normal distribution to determine the safety stock for a product. The Z value of 1.65 would be associated with what service level?

- A) 90 percent
- B) 95 percent
- C) 100 percent
- D) 92.5 percent
- E) None of the above

Answer: BDiff: 2Topic: USE OF SAFETY STOCK 75) A person is using the normal distribution to determine the safety stock for a product. The Z value of 2.33 would be associated with what service level?

- A) 95 percent
- B) 97.5 percent
- C) 98 percent
- D) 99 percent
- E) None of the above

Answer: DDiff: 2Topic: USE OF SAFETY STOCK 76) Rolf Steps is the production manager for a local manufacturing firm. This company produces staplers and other items. The annual demand for a particular stapler is 1,600 units. The holding cost is $2 per unit per year. The cost of setting up the production line is $25. There are 200 working days per year. The production rate for this product is 80 per day. If Rolf decided to produce 200 units each time he started production of the stapler, what would his maximum inventory level be?

- A) 200
- B) 180
- C) 100
- D) 90
- E) None of the above

Answer: BDiff: 3Topic: EOQ WITHOUT THE INSTANTANEOUS RECEIPT ASSUMPTIONAACSB: Analytic Skills77) In the ABC analysis of inventory, the A group items

- A) are critical to the functioning of the organization.
- B) are the most expensive class of items.
- C) typically account for over 70 percent of the company’s business in dollars.
- D) typically account for about 10 percent of a company’s inventory items.
- E) All of the above

Answer: EDiff: 2Topic: ABC ANALYSIS 78) Which of the following statements concerning ABC analysis is false?

- A) Class B items typically account for 20 percent of the company’s business in dollars.
- B) There are typically less class A items in stock than class B.
- C) Class C items typically account for 70 percent of the company’s inventory items.
- D) Class C items tend to have more complex inventory policies than Class B items.
- E) Class B items typically account for 20 percent of the company’s business in dollars.

Answer: DDiff: 2Topic: ABC ANALYSIS 79) With an annual demand of 2,400 units, daily demand of 10 units, and daily production rate of 40 units, a company has determined that each production run will be for 200 units. If production starts when the inventory level is at zero, how many units would actually be in the warehouse at the end of the first day of production? (Round your answer to the nearest unit.)

- A) 12
- B) 20
- C) 30
- D) 40
- E) None of the above

Answer: CDiff: 2Topic: EOQ WITHOUT THE INSTANTANEOUS RECEIPT ASSUMPTIONAACSB: Analytic Skills 80) Jack Spratt is the production manager for a manufacturing firm that produces wizzy-gadgets and other items. The annual demand for a particular wizzy-gadget is 1,600 units. The holding cost is $2 per unit per year. The cost of setting up the production line is $25. There are 200 working days per year. The production rate for this product is 80 per day. If his maximum inventory level is 180 units, how many units did he produce each time he started production of the wizzy-gadgets?

- A) 200
- B) 180
- C) 100
- D) 90
- E) None of the above

Answer: ADiff: 3Topic: EOQ WITHOUT THE INSTANTANEOUS RECEIPT ASSUMPTIONAACSB: Analytic Skills81) Rose Arena is the production manager for a manufacturing firm that produces buggy whips and other items. The annual demand for a particular buggy whip is 1,600 units. The holding cost is $2 per unit per year. The cost of setting up the production line is $25. There are 200 working days per year. Rose decided to produce 200 units each time she started production of the buggy whips. If it took her 4 days to produce the 200 units, what was her production rate?

- A) 80 units/day
- B) 60 units/day
- C) 50 units/day
- D) 100 units/day
- E) 40 units/day

Answer: CDiff: 1Topic: EOQ WITHOUT THE INSTANTANEOUS RECEIPT ASSUMPTIONAACSB: Analytic Skills 82) An organization hosting a 5K race is looking to sell t-shirts at the event. Demand for t-shirts is believed to be normally distributed with a mean of 100 and standard deviation of 15. With a marginal loss of $4 and marginal profit of $5, how many t-shirts should the organization stock for the 5K race?

- A) 98
- B) 85
- C) 103
- D) 115
- E) 113

Answer: CDiff: 3Topic: SINGLE-PERIOD INVENTORY MODELSAACSB: Analytic Skills 83) A bakery must decide how many loaves of fresh bread to produce in a single day. Daily demand for fresh bread is normally distributed with a mean of 70 loaves and standard deviation of 18. If the marginal loss is $2 and the marginal profit is $1, how much bread should the bakery produce in a single day?

- A) 88
- B) 52
- C) 63
- D) 78
- E) 70

Answer: CDiff: 3Topic: SINGLE-PERIOD INVENTORY MODELSAACSB: Analytic Skills 84) Which of the following statements about the kanban system is __false__?

- A) Kanban in Japanese means “card.”
- B) In a dual card system, there is the C-kanban and P-
- C) More than two containers can be used.
- D) The kanban system is most commonly executed manually.
- E) One typical kanban rule is that no containers are filled without the appropriate C-

Answer: EDiff: 2Topic: JUST-IN-TIME INVENTORY CONTROL85) East Valve Distributors distributes industrial valves and control devices. The Eastern control device has an annual demand of 9,375 units and sells for $100 per unit. The cost of ordering is $160 per order and the average carrying cost per unit per year is $0.75. Determine the economic order quantity.Answer: EOQ = 2,000 unitsDiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDERAACSB: Analytic Skills 86) A company annually uses 1,200 of a certain spare part that costs $25 for each order and has a $24 annual holding cost. Calculate the total annual cost for order sizes of: 25, 40, 50, 60, and 100. Identify the economic order quantity, and consider the implications for making an error in calculating the economic order quantity.Answer: Total Cost = total ordering cost + total holding costQ = 25 TC = 1200 + 300 = $1,500Q = 40 TC = 750 + 480 = $1,230Q = 50 TC = 600 + 600 = $1,200Q = 60 TC = 500 + 720 = $1,220Q = 100 TC = 300 + 1200 = $1,500Q* = [(2 × 1200 × 25)/24]1/2 = 50 units per orderSmall variations in order quantity will not have a significant impact on total costs.Diff: 3Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDERAACSB: Analytic Skills 87) David and Beth Sheba run a health food store. Their top selling item is called Heavenly Kelp. The annual demand for this is 810 units, and demand is constant throughout the year. The cost of placing an order is $20, while the holding cost per unit per year is $4.(a) How many orders per year should be placed if they wish to minimize their total cost?(b) What is the minimum possible annual holding and ordering cost?Answer:(a) EOQ = 90 units. Therefore, the number of orders per year is 810/90 = 9 orders per year.(b) (90/2)4 + 9($20) = $360 total costDiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDERAACSB: Analytic Skills 88) Everett Mann’s Dream Store sells waterbeds and supplies. The best selling bed in the store has an annual demand of 400 units. The ordering cost is $40, while the holding cost is $5 per unit per year. There are 250 working days per year, and the lead-time is 6 days.(a) To minimize total cost, how many units should be ordered each time an order is placed?(b) If the holding cost per unit was $6 instead of $5, what would the optimal order quantity be?Answer:(a) EOQ = 80 units(b) EOQ = 73.03 units if *C*h=6.Diff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDERAACSB: Analytic Skills89) Ivonne Callen sells beauty supplies. Her annual demand for a particular skin lotion is 1,000 units. The cost of placing an order is $20, while the holding cost per unit per year is 10 percent of the cost. This item currently costs $10 if the order quantity is less than 300. For orders of 300 units or more, the cost falls to $9.80. To minimize total cost, how many units should Ivonne order each time she places an order? What is the minimum total cost?Answer: With EOQ = 200, the total cost is $10,200.With Q = 300 to obtain discount, the total cost is $10,013.67.Therefore, she should order 300 units.Diff: 3Topic: QUANTITY DISCOUNT MODELSAACSB: Analytic Skills 90) Suppose that lead-time demand is normally distributed with a mean of 100 units and a standard deviation of 20 units. If a firm wants to maintain a 97% service level, what should the reorder point be?Answer: 100 + 1.88(20) = 137.6 unitsDiff: 2Topic: USE OF SAFETY STOCKAACSB: Analytic Skills 91) ArtOrgan, Ltd. distributes mechanical replacements for human mitral heart valves. Its artificial valve has a demand of 12,765 units per year and sells for $7,900 per unit. The cost of ordering is $75 per order and the average carrying cost per unit per year is $150. Determine the economic order quantity.Answer: EOQ = 113 unitsDiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDERAACSB: Analytic Skills 92) Furniture Manufacturers Inc., uses 20,000 loads of lumber per year. A load of lumber costs $500 and the carrying cost is 10 percent of the unit cost. The cost to order is $200 per order and the lead-time is three working days. Assuming 200 working days, determine:(a) the economic order quantity.(b) the reorder point.(c) number of orders per year.(d) working days between orders.Answer:(a) EOQ = 400 units(b) ROP = 100(3) = 300 units(c) number of orders per year = D/Q = 20,000/400 = 50 orders(d) working days between orders = 200/50 = 4 daysDiff: 3Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDER and REORDER POINT: DETERMINING WHEN TO ORDERAACSB: Analytic Skills93) A company uses 1,500 per year of a certain subassembly that has an annual holding cost of $45 per unit. Each order placed costs $150. The company operates 300 days per year and it has found that an order must be placed with the supplier 6 working days before it can expect to receive that order. For this subassembly, find:(a) the economic order quantity.(b) the annual holding cost.(c) the annual ordering cost.(d) the reorder point.Answer:(a) EOQ = 100(b) annual holding cost = (100/2)(45) = 2250(c) annual ordering cost = (1500/100)(150) = 2250(d) ROP = 5(6) = 30 unitsDiff: 3Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDER and REORDER POINT: DETERMINING WHEN TO ORDERAACSB: Analytic Skills 94) The H.A.L. Computer Store sells a printer for $200. Demand for this is constant during the year, and annual demand is forecasted to be 600 units. The holding cost is $20 per unit per year, while the cost of ordering is $60 per order. Currently, the company is ordering 12 times per year (50 units each time). There are 250 working days per year and the lead-time is 10 days.(a) Given the current policy of ordering 50 units at a time, what is the total of the annual ordering cost and the annual holding cost?(b) If the company used the absolute best inventory policy, what would the total of the ordering and holding cost be?(c) What is the reorder point?Answer:(a) TOC + THC = 720 + 500 = $1220(b) If they order EOQ = 60 units, TOC + THC = 600 + 600 = $1,200(c) ROP = (600/250)10 = 24 unitsDiff: 3Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDER and REORDER POINT: DETERMINING WHEN TO ORDERAACSB: Analytic Skills 95) Purinnerds Dog Food is a very popular product at Kay Gnein’s corner grocery. Demand for this is relatively constant, and the total demand for the year is 1,200 bags. The cost of placing an order is $50, while the holding cost is $3 per unit per year. The store is open 300 days per year. Lead-time for this is 8 days.(a) If Kay places 50 orders per year, what would her annual ordering and holding costs be?(b) If Kay wishes to minimize her total inventory cost, how many units should she order each time an order is placed?(c) What is the reorder point?Answer:(a) With 50 orders per year, Q=24. TC = TOC + THC = 2500 + 36 = $2,536(b) EOQ = 200(c) ROP = (1200/300)8 = 32 unitsDiff: 3Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDER and REORDER POINT: DETERMINING WHEN TO ORDERAACSB: Analytic Skills96) A company uses 2,750 per year of a certain subassembly that has a purchase cost of $450, and an annual holding cost of $500 per unit. Each order placed costs $150. The company operates 300 days per year and it has found that an order must be placed with the supplier 12 working days before it can expect to receive that order. For this subassembly, find:(a) the economic order quantity.(b) the reorder point.Answer:(a) [2(2750)(150)/500]1/2 = 40.6 units(b) (2750/300)(12) = 110 unitsDiff: 2Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDER and REORDER POINT: DETERMINING WHEN TO ORDERAACSB: Analytic Skills 97) The H.A.L. Computer Store sells a printer for $400. Demand for this is constant during the year, and annual demand is forecasted to be 1350 units. The holding cost is $20 per unit per year, while the cost of ordering is $90 per order. Currently, the company is ordering 12 times per year (92 units each time). There are 270 working days per year and the lead-time is 8 days. What should be the reorder point?Answer: (1350/270)(8) = 40 unitsDiff: 2Topic: REORDER POINT: DETERMINING WHEN TO ORDERAACSB: Analytic Skills 98) The Handy Manufacturing Company manufactures small air conditioner compressors. The estimated demand for the year is 12,000 units. The setup cost for the production process is $200 per run, and the carrying cost is $10.00 per unit per year. The daily production rate is 100 units per day, and demand has been 50 units per day. Determine the number of units to produce in each batch. (The problem assumes 240 operating days.)Answer: Optimum production quantity = {[2(12,000)(200)]/[10(1−50/100)]1/2 = 979.8 unitsDiff: 2Topic: EOQ WITHOUT THE INSTANTANEOUS RECEIPT ASSUMPTIONAACSB: Analytic Skills 99) Anne Beck recently took over a beauty supply store. Her predecessor always ordered shampoo in quantities of 100 units. Anne is reevaluating this policy. Based on her analysis, the cost to place each order is $35 and the holding cost is $8 per shampoo bottle per year. The annual demand for this product is 2500 bottles. Should Anne change the current order policy and, if so, how much can she save?Answer: Current inventory policy parameters:D = 2500, Q = 100, # of orders = 25, Average inventory = 50, Order cost = $875,Holding cost = $400, Total inventory cost = $875 + $400 = $1,275 Optimal inventory policy parameters:Q* = 147.9, or 148 bottles, # of orders = 16.89, Average inventory = 74, Order cost = $591.15,Holding cost = $592, Total inventory cost = $591.15 + $592 = $1,183.15 She should change her order policy.Savings = $1,275 – $1,183.15 = $91.85Diff: 3Topic: ECONOMIC ORDER QUANTITY: DETERMINING HOW MUCH TO ORDERAACSB: Analytic Skills100) Candy Incorporated stocks bubble gum game cards, an item that has a normally distributed demand during the reorder period with a mean of 12 dozen boxes and a standard deviation of two dozen boxes. If it is desirable to experience a stockout only 10 percent of the time, what is the appropriate safety stock?Answer: For 90 percent service level, the safety stock = 1.28(2) = 2.56 units.Diff: 2Topic: USE OF SAFETY STOCKAACSB: Analytic Skills 101) The purchasing manager for a firm is trying to determine what the safety stock should be for a particular product. She has developed the following table, which gives the distribution of demand during the lead-time and the probabilities:

Demand DuringLead-Time | Probability |

40 | 0.20 |

50 | 0.25 |

60 | 0.25 |

70 | 0.20 |

80 | 0.10 |

The carrying cost is $5 per unit per year, the ordering cost is $30 per order, and the stockout cost is $40 per unit. The reorder point is 60 units, and 6 orders are placed each year. What level of safety stock should be maintained?Answer:

Safety Stock | Additional Holding Cost | Stockout Cost | Total Cost |

0 | 0 | (10)(0.2)(40)(10)+(20)(0.1)(40)(10) | 1600 |

10 | 50 | (10)(0.1)(40)(10) | 450 |

20 | 100 | 0 | 100 |

Therefore, 20 units of safety stock should be carried.Diff: 3Topic: USE OF SAFETY STOCKAACSB: Analytic Skills 102) A professional baseball organization chooses to sell game day programs. Demand for game day programs is normally distributed with a mean of 2,000 and standard deviation of 300. If the marginal loss is $1 and the marginal profit is $3, how many programs should the baseball organization print?Answer: *P* = ML/(ML+MP) = 0.25. Z = 0.6745. X = 2,000 + 0.6745(300) = 2202.35.Therefore, the baseball organization should print 2203 programs.Diff: 3Topic: SINGLE-PERIOD INVENTORY MODELSAACSB: Analytic Skills103) Demand for local newspapers in King County during weekdays is normally distributed with a mean of 500 and standard deviation of 100. The marginal loss per paper is $0.10 and marginal profit is $0.40. How many newspapers should the local publisher produce each day?Answer: *P* = ML/(ML+MP) = 0.20. Z = 0.8416. X = 1,000 + 0.8416(100) = 1,084.16.Therefore, the newspaper organization should print 1085 newspapers.Diff: 3Topic: SINGLE-PERIOD INVENTORY MODELSAACSB: Analytic Skills 104) Consider the material structure tree for item A below. Assume 15 units of A are needed. (a) How many units of B are needed?(b) How many units of C are needed?(c) How many units of D are needed?(d) How many units of E are needed?Answer: (a) 3*15 = 45. (b) 4*15 = 60. (c) 3*3*15+2*4*15 = 255. (d) 5*3*15+6*4*15 = 585Diff: 2Topic: DEPENDENT DEMAND: THE CASE FOR MATERIAL REQUIREMENTS PLANNINGAACSB: Analytic Skills 105) Explain the purpose of ABC analysis.Answer: The purpose of ABC analysis is to divide all of a company’s inventory items into three groups (group A, group B, and group C) based on the overall inventory value of the items. A prudent manager should spend more time managing those items representing the greatest dollar inventory cost (A items) because this is where the greatest potential savings are.Diff: 2Topic: ABC ANALYSIS 106) List three general categories of inventory.Answer: raw material, work-in-process inventory, finished goods inventoryDiff: 2Topic: INTRODUCTION107) Explain how inventory can act as a buffer in the production process.Answer: Storing some inventory helps to decouple the manufacturing process within the organization.Diff: 2Topic: IMPORTANCE OF INVENTORY CONTROL 108) List several disadvantages of buying inventory in large quantities.Answer: higher storage cost, more spoilage, damaged stock, theft, insurance, less cash to investDiff: 2Topic: IMPORTANCE OF INVENTORY CONTROL 109) List four significant inventory costs.Answer: (1) cost of the items (purchase cost or material cost), (2) cost of ordering, (3) cost of carrying, or holding, inventory, and (4) cost of stockoutsDiff: 2Topic: INVENTORY DECISIONS 110) List major carrying cost factors.Answer: cost of capital, taxes, insurance, spoilage, theft, obsolescence, warehouse personnel wages, utilities and building costs for the warehouse, and supplies such as forms and paper for the warehouseDiff: 2Topic: INVENTORY DECISIONS 111) List major ordering cost factors.Answer: developing and sending purchase orders, processing and inspecting incoming inventory, bill paying, inventory inquiries, and purchasing department expenses and suppliesDiff: 2Topic: INVENTORY DECISIONS 112) Explain the basic difference(s) between the simple EOQ model and the production run model.Answer: In the simple EOQ, inventory delivery is assumed to occur instantaneously, while in the production run model, inventory is assumed to be produced (or “delivered”) over time.Diff: 2Topic: EOQ WITHOUT THE INSTANTANEOUS RECEIPT ASSUMPTION 113) Discuss why it is sometimes prudent not to order the minimum level required to obtain a quantity discount.Answer: The increased holding cost associated with ordering the minimum level required for the discount may outweigh the savings from the quantity discount.Diff: 2Topic: QUANTITY DISCOUNT MODELS *Quantitative Analysis for Management, 11e*** (Render)****Chapter 7 Linear Programming Models: Graphical and Computer Methods**** **1) Management resources that need control include machinery usage, labor volume, money spent, time used, warehouse space used, and material usage.Answer: TRUEDiff: 1Topic: INTRODUCTION 2) In the term linear programming, the word programming comes from the phrase “computer programming.”Answer: FALSEDiff: 2Topic: INTRODUCTION 3) One of the assumptions of LP is “simultaneity.”Answer: FALSEDiff: 2Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 4) Any linear programming problem can be solved using the graphical solution procedure.Answer: FALSEDiff: 1Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM 5) An LP formulation typically requires finding the maximum value of an objective while simultaneously maximizing usage of the resource constraints.Answer: FALSEDiff: 2Topic: FORMULATING LP PROBLEMS 6) There are no limitations on the number of constraints or variables that can be graphed to solve an LP problem.Answer: FALSEDiff: 1Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM 7) Resource restrictions are called constraints.Answer: TRUEDiff: 1Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 8) One of the assumptions of LP is “proportionality.”Answer: TRUEDiff: 2Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 9) The set of solution points that satisfies all of a linear programming problem’s constraints simultaneously is defined as the feasible region in graphical linear programming.Answer: TRUEDiff: 2Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM 10) An objective function is necessary in a maximization problem but is not required in a minimization problem.Answer: FALSEDiff: 1Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 11) In some instances, an infeasible solution may be the optimum found by the corner point method.Answer: FALSEDiff: 2Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM 12) The rationality assumption implies that solutions need not be in whole numbers (integers).Answer: FALSEDiff: 2Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 13) The solution to a linear programming problem must always lie on a constraint.Answer: TRUEDiff: 2Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM 14) In a linear program, the constraints must be linear, but the objective function may be nonlinear.Answer: FALSEDiff: 2Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 15) Resource mix problems use LP to decide how much of each product to make, given a series of resource restrictions.Answer: FALSEDiff: 2Topic: FORMULATING LP PROBLEMS 16) The existence of non-negativity constraints in a two-variable linear program implies that we are always working in the northwest quadrant of a graph.Answer: FALSEDiff: 2Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM 17) In linear programming terminology, “dual price” and “sensitivity price” are synonyms.Answer: FALSEDiff: 2Topic: SENSITIVITY ANALYSIS 18) Any time that we have an isoprofit line that is parallel to a constraint, we have the possibility of multiple solutions.Answer: TRUEDiff: 2Topic: FOUR SPECIAL CASES IN LP 19) If the isoprofit line is not parallel to a constraint, then the solution must be unique.Answer: TRUEDiff: 2Topic: FOUR SPECIAL CASES IN LPAACSB: Reflective Thinking 20) When two or more constraints conflict with one another, we have a condition called unboundedness.Answer: FALSEDiff: 2Topic: FOUR SPECIAL CASES IN LP 21) The addition of a redundant constraint lowers the isoprofit line.Answer: FALSEDiff: 2Topic: FOUR SPECIAL CASES IN LP 22) Sensitivity analysis enables us to look at the effects of changing the coefficients in the objective function, one at a time.Answer: TRUEDiff: 2Topic: SENSITIVITY ANALYSIS 23) A widely used mathematical programming technique designed to help managers and decision making relative to resource allocation is called ________.

- A) linear programming
- B) computer programming
- C) constraint programming
- D) goal programming
- E) None of the above

Answer: ADiff: 1Topic: INTRODUCTION 24) Typical resources of an organization include ________.

- A) machinery usage
- B) labor volume
- C) warehouse space utilization
- D) raw material usage
- E) All of the above

Answer: EDiff: 1Topic: INTRODUCTION 25) Which of the following is __not__ a property of all linear programming problems?

- A) the presence of restrictions
- B) optimization of some objective
- C) a computer program
- D) alternate courses of action to choose from
- E) usage of only linear equations and inequalities

Answer: CDiff: 2Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 26) A feasible solution to a linear programming problem

- A) must be a corner point of the feasible region.
- B) must satisfy all of the problem’s constraints simultaneously.
- C) need not satisfy all of the constraints, only the non-negativity constraints.
- D) must give the maximum possible profit.
- E) must give the minimum possible cost.

Answer: BDiff: 2Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM 27) Infeasibility in a linear programming problem occurs when

- A) there is an infinite solution.
- B) a constraint is redundant.
- C) more than one solution is optimal.
- D) the feasible region is unbounded.
- E) there is no solution that satisfies all the constraints given.

Answer: EDiff: 2Topic: FOUR SPECIAL CASES IN LP 28) In a maximization problem, when one or more of the solution variables and the profit can be made infinitely large without violating any constraints, the linear program has

- A) an infeasible solution.
- B) an unbounded solution.
- C) a redundant constraint.
- D) alternate optimal solutions.
- E) None of the above

Answer: BDiff: 2Topic: FOUR SPECIAL CASES IN LP 29) Which of the following is __not__ a part of every linear programming problem formulation?

- A) an objective function
- B) a set of constraints
- C) non-negativity constraints
- D) a redundant constraint
- E) maximization or minimization of a linear function

Answer: DDiff: 2Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM30) When appropriate, the optimal solution to a maximization linear programming problem can be found by graphing the feasible region and

- A) finding the profit at every corner point of the feasible region to see which one gives the highest value.
- B) moving the isoprofit lines towards the origin in a parallel fashion until the last point in the feasible region is encountered.
- C) locating the point that is highest on the graph.
- D) None of the above
- E) All of the above

Answer: ADiff: 2Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM 31) The mathematical theory behind linear programming states that an optimal solution to any problem will lie at a(n) ________ of the feasible region.

- A) interior point or center
- B) maximum point or minimum point
- C) corner point or extreme point
- D) interior point or extreme point
- E) None of the above

Answer: CDiff: 1Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM 32) Which of the following is __not__ a property of linear programs?

- A) one objective function
- B) at least two separate feasible regions
- C) alternative courses of action
- D) one or more constraints
- E) objective function and constraints are linear

Answer: BDiff: 1Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 33) The corner point solution method

- A) will always provide one, and only one, optimum.
- B) will yield different results from the isoprofit line solution method.
- C) requires that the profit from all corners of the feasible region be compared.
- D) requires that all corners created by all constraints be compared.
- E) will not provide a solution at an intersection or corner where a non-negativity constraint is involved.

Answer: CDiff: 2Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM 34) When a constraint line bounding a feasible region has the same slope as an isoprofit line,

- A) there may be more than one optimum solution.
- B) the problem involves redundancy.
- C) an error has been made in the problem formulation.
- D) a condition of infeasibility exists.
- E) None of the above

Answer: ADiff: 2Topic: FOUR SPECIAL CASES IN LP 35) The simultaneous equation method is

- A) an alternative to the corner point method.
- B) useful only in minimization methods.
- C) an algebraic means for solving the intersection of two or more constraint equations.
- D) useful only when more than two product variables exist in a product mix problem.
- E) None of the above

Answer: CDiff: 2Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM 36) Consider the following linear programming problem: The maximum possible value for the objective function is

- A) 360.
- B) 480.
- C) 1520.
- D) 1560.
- E) None of the above

Answer: CDiff: 3Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 37) Consider the following linear programming problem: The feasible corner points are (48,84), (0,120), (0,0), (90,0). What is the maximum possible value for the objective function?

- A) 1032
- B) 1200
- C) 360
- D) 1600
- E) None of the above

Answer: BDiff: 2Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 38) Consider the following linear programming problem: Which of the following points (X,Y) is not a feasible corner point?

- A) (0,60)
- B) (105,0)
- C) (120,0)
- D) (100,10)
- E) None of the above

Answer: CDiff: 2Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 39) Consider the following linear programming problem: Which of the following points (X,Y) is not feasible?

- A) (50,40)
- B) (20,50)
- C) (60,30)
- D) (90,10)
- E) None of the above

Answer: ADiff: 2Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 40) Two models of a product — Regular (X) and Deluxe (Y) — are produced by a company. A linear programming model is used to determine the production schedule. The formulation is as follows: The optimal solution is X = 100, Y = 0. How many units of the regular model would be produced based on this solution?

- A) 0
- B) 100
- C) 50
- D) 120
- E) None of the above

Answer: BDiff: 1Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 41) Two models of a product — Regular (X) and Deluxe (Y) — are produced by a company. A linear programming model is used to determine the production schedule. The formulation is as follows: The optimal solution is X=100, Y=0. Which of these constraints is redundant?

- A) the first constraint
- B) the second constraint
- C) the third constraint
- D) All of the above
- E) None of the above

Answer: BDiff: 3Topic: FOUR SPECIAL CASES IN LPAACSB: Analytic Skills 42) Consider the following linear programming problem: What is the optimum solution to this problem (X,Y)?

- A) (0,0)
- B) (50,0)
- C) (0,100)
- D) (400,0)
- E) None of the above

Answer: BDiff: 3Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 43) Consider the following linear programming problem: This is a special case of a linear programming problem in which

- A) there is no feasible solution.
- B) there is a redundant constraint.
- C) there are multiple optimal solutions.
- D) this cannot be solved graphically.
- E) None of the above

Answer: EDiff: 3Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 44) Consider the following linear programming problem: This is a special case of a linear programming problem in which

- A) there is no feasible solution.
- B) there is a redundant constraint.
- C) there are multiple optimal solutions.
- D) this cannot be solved graphically.
- E) None of the above

Answer: ADiff: 3Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 45) Which of the following is __not__ acceptable as a constraint in a linear programming problem (maximization)?

- A) Constraint 1
- B) Constraint 2
- C) Constraint 3
- D) Constraint 4
- E) None of the above

Answer: ADiff: 2Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM46) If one changes the contribution rates in the objective function of an LP,

- A) the feasible region will change.
- B) the slope of the isoprofit or isocost line will change.
- C) the optimal solution to the LP is sure to no longer be optimal.
- D) All of the above
- E) None of the above

Answer: BDiff: 2Topic: SENSITIVITY ANALYSIS 47) Sensitivity analysis may also be called

- A) postoptimality analysis.
- B) parametric programming.
- C) optimality analysis.
- D) All of the above
- E) None of the above

Answer: DDiff: 2Topic: SENSITIVITY ANALYSIS 48) Sensitivity analyses are used to examine the effects of changes in

- A) contribution rates for each variable.
- B) technological coefficients.
- C) available resources.
- D) All of the above
- E) None of the above

Answer: DDiff: 2Topic: SENSITIVITY ANALYSIS 49) Which of the following is a basic assumption of linear programming?

- A) The condition of uncertainty exists.
- B) Independence exists for the activities.
- C) Proportionality exists in the objective function and constraints.
- D) Divisibility does not exist, allowing only integer solutions.
- E) Solutions or variables may take values from -∞ to +∞.

Answer: CDiff: 2Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 50) The condition when there is no solution that satisfies all the constraints simultaneously is called

- A) boundedness.
- B) redundancy.
- C) optimality.
- D) dependency.
- E) None of the above

Answer: EDiff: 2Topic: FOUR SPECIAL CASES IN LP51) If the addition of a constraint to a linear programming problem does not change the solution, the constraint is said to be

- A) unbounded.
- B) non-
- C) infeasible.
- D) redundant.
- E) bounded.

Answer: DDiff: 2Topic: FOUR SPECIAL CASES IN LP 52) Which of the following is __not__ an assumption of LP?

- A) simultaneity
- B) certainty
- C) proportionality
- D) divisibility
- E) additivity

Answer: ADiff: 2Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 53) The difference between the left-hand side and right-hand side of a less-than-or-equal-to constraint is referred to as

- A) surplus.
- B) constraint.
- C) slack.
- D) shadow price.
- E) None of the above

Answer: CDiff: 2Topic: LINEAR PROGRAMMING MODELS: GRAPHICAL AND COMPUTER METHODS 54) The difference between the left-hand side and right-hand side of a greater-than-or-equal-to constraint is referred to as

- A) surplus.
- B) constraint.
- C) slack.
- D) shadow price.
- E) None of the above

Answer: ADiff: 2Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM 55) A constraint with zero slack or surplus is called a

- A) nonbinding constraint.
- B) resource constraint.
- C) binding constraint.
- D) nonlinear constraint.
- E) linear constraint.

Answer: CDiff: 1Topic: SOLVING FLAIR FURNITURE’S LP PROBLEM USING QM FOR WINDOWS AND EXCEL56) A constraint with positive slack or surplus is called a

- A) nonbinding constraint.
- B) resource constraint.
- C) binding constraint.
- D) nonlinear constraint.
- E) linear constraint.

Answer: ADiff: 1Topic: SOLVING FLAIR FURNITURE’S LP PROBLEM USING QM FOR WINDOWS AND EXCEL 57) The increase in the objective function value that results from a one-unit increase in the right-hand side of that constraint is called

- A) surplus.
- B) shadow price.
- C) slack.
- D) dual price.
- E) None of the above

Answer: BDiff: 2Topic: SENSITIVITY ANALYSIS 58) A straight line representing all non-negative combinations of *X*1 and *X*2 for a particular profit level is called a(n)

- A) constraint line.
- B) objective line.
- C) sensitivity line.
- D) profit line.
- E) isoprofit line.

Answer: EDiff: 2Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM 59) In order for a linear programming problem to have a unique solution, the solution must exist

- A) at the intersection of the non-negativity constraints.
- B) at the intersection of a non-negativity constraint and a resource constraint.
- C) at the intersection of the objective function and a constraint.
- D) at the intersection of two or more constraints.
- E) None of the above

Answer: DDiff: 2Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM 60) In order for a linear programming problem to have multiple solutions, the solution must exist

- A) at the intersection of the non-negativity constraints.
- B) on a non-redundant constraint parallel to the objective function.
- C) at the intersection of the objective function and a constraint.
- D) at the intersection of three or more constraints.
- E) None of the above

Answer: BDiff: 2Topic: FOUR SPECIAL CASES IN LP 61) Consider the following linear programming problem: The maximum possible value for the objective function is

- A) 360.
- B) 480.
- C) 1520.
- D) 1560.
- E) None of the above

Answer: EDiff: 3Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 62) Consider the following linear programming problem: Which of the following points (X,Y) is feasible?

- A) (10,120)
- B) (120,10)
- C) (30,100)
- D) (60,90)
- E) None of the above

Answer: CDiff: 2Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 63) Consider the following linear programming problem: Which of the following points (X,Y) is in the feasible region?

- A) (30,60)
- B) (105,5)
- C) (0,210)
- D) (100,10)
- E) None of the above

Answer: DDiff: 2Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills64) Consider the following linear programming problem: Which of the following points (X,Y) is feasible?

- A) (50,40)
- B) (30,50)
- C) (60,30)
- D) (90,20)
- E) None of the above

Answer: CDiff: 2Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 65) Which of the following is __not__ an assumption of LP?

- A) certainty
- B) proportionality
- C) divisibility
- D) multiplicativity
- E) additivity

Answer: DDiff: 2Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 66) Consider the following linear programming problem: This is a special case of a linear programming problem in which

- A) there is no feasible solution.
- B) there is a redundant constraint.
- C) there are multiple optimal solutions.
- D) this cannot be solved graphically.
- E) None of the above

Answer: BDiff: 3Topic: FOUR SPECIAL CASES IN LPAACSB: Analytic Skills67) Which of the following functions is __not__ linear?

- A) 5X + 3Z
- B) 3X + 4Y + Z – 3
- C) 2X + 5YZ
- D) Z
- E) 2X – 5Y + 2Z

Answer: CDiff: 1Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 68) Which of the following is __not__ one of the steps in formulating a linear program?

- A) Graph the constraints to determine the feasible region.
- B) Define the decision variables.
- C) Use the decision variables to write mathematical expressions for the objective function and the constraints.
- D) Identify the objective and the constraints.
- E) Completely understand the managerial problem being faced.

Answer: ADiff: 2Topic: FORMULATING LP PROBLEMS 69) Which of the following is __not__ acceptable as a constraint in a linear programming problem (minimization)?

- A) Constraint 1
- B) Constraint 2
- C) Constraint 3
- D) Constraint 4
- E) Constraint 5

Answer: EDiff: 2Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 70) What type of problems use LP to decide how much of each product to make, given a series of resource restrictions?

- A) resource mix
- B) resource restriction
- C) product restriction
- D) resource allocation
- E) product mix

Answer: EDiff: 2Topic: FORMULATING LP PROBLEMS71) Consider the following linear programming problem: This is a special case of a linear programming problem in which

- A) there is no feasible solution.
- B) there is a redundant constraint.
- C) there are multiple optimal solutions.
- D) this cannot be solved graphically.
- E) None of the above

Answer: BDiff: 3Topic: FOUR SPECIAL CASES IN LPAACSB: Analytic Skills 72) Consider the following constraints from a linear programming problem: 2X + Y ≤ 200X + 2Y ≤ 200X, Y ≥ 0 If these are the only constraints, which of the following points (X,Y) __cannot__ be the optimal solution?

- A) (0, 0)
- B) (0, 200)
- C) (0,100)
- D) (100, 0)
- E) (66.67, 66.67)

Answer: BDiff: 3Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 73) Consider the following constraints from a linear programming problem: 2X + Y ≤ 200X + 2Y ≤ 200X, Y ≥ 0 If these are the only constraints, which of the following points (X,Y) cannot be the optimal solution?

- A) (0, 0)
- B) (0, 100)
- C) (65, 65)
- D) (100, 0)
- E) (66.67, 66.67)

Answer: CDiff: 3Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills74) A furniture company is producing two types of furniture. Product A requires 8 board feet of wood and 2 lbs of wicker. Product B requires 6 board feet of wood and 6 lbs of wicker. There are 2000 board feet of wood available for product and 1000 lbs of wicker. Product A earns a profit margin of $30 a unit and Product B earns a profit margin of $40 a unit. Formulate the problem as a linear program.Answer: Diff: 2Topic: FORMULATING LP PROBLEMSAACSB: Analytic Skills 75) As a supervisor of a production department, you must decide the daily production totals of a certain product that has two models, the Deluxe and the Special. The profit on the Deluxe model is $12 per unit and the Special’s profit is $10. Each model goes through two phases in the production process, and there are only 100 hours available daily at the construction stage and only 80 hours available at the finishing and inspection stage. Each Deluxe model requires 20 minutes of construction time and 10 minutes of finishing and inspection time. Each Special model requires 15 minutes of construction time and 15 minutes of finishing and inspection time. The company has also decided that the Special model must comprise at least 40 percent of the production total. (a) Formulate this as a linear programming problem.(b) Find the solution that gives the maximum profit.Answer: (b) Optimal solution: X1 = 120, X2 = 240 Profit = $3,840Diff: 3Topic: FORMULATING LP PROBLEMS and GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 76) The Fido Dog Food Company wishes to introduce a new brand of dog biscuits (composed of chicken and liver-flavored biscuits) that meets certain nutritional requirements. The liver-flavored biscuits contain 1 unit of nutrient A and 2 units of nutrient B, while the chicken-flavored ones contain 1 unit of nutrient A and 4 units of nutrient B. According to federal requirements, there must be at least 40 units of nutrient A and 60 units of nutrient B in a package of the new biscuit mix. In addition, the company has decided that there can be no more than 15 liver-flavored biscuits in a package. If it costs 1 cent to make a liver-flavored biscuit and 2 cents to make a chicken-flavored one, what is the optimal product mix for a package of the biscuits in order to minimize the firm’s cost?(a) Formulate this as a linear programming problem.(b) Find the optimal solution for this problem graphically.(c) Are any constraints redundant? If so, which one or ones?(d) What is the total cost of a package of dog biscuits using the optimal mix?Answer: (b) Corner points (0,40) and (15,25)Optimal solution is (15,25) with cost of 65. (c) 2X1 + 4X2 ≥ 60 is redundant. (d) minimum cost = 65 centsDiff: 3Topic: FORMULATING LP PROBLEMS and GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 77) Consider the following linear program: (a) Solve the problem graphically. Is there more than one optimal solution? Explain.(b) Are there any redundant constraints?Answer:(a) Corner points (0,50), (0,200), (50,50), (75,75), (50,150)Optimum solutions: (75,75) and (50,150). Both yield a profit of $3,000.(b) The constraint X1 ≤ 100 is redundant since 3X1 + X2 ≤ 300 also means that X1 cannot exceed 100.Diff: 3Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 78) Solve the following linear programming problem using the corner point method: Answer: Feasible corner points (X,Y): (0,3) (0,10) (2.4,8.8) (6.75,3)Maximum profit 70.5 at (6.75,3).Diff: 3Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 79) Solve the following linear programming problem using the corner point method: Answer: Feasible corner points (X,Y): (0,2) (0,10) (4,8) (10,2)Maximum profit is 52 at (4,8).Diff: 3Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 80) Billy Penny is trying to determine how many units of two types of lawn mowers to produce each day. One of these is the Standard model, while the other is the Deluxe model. The profit per unit on the Standard model is $60, while the profit per unit on the Deluxe model is $40. The Standard model requires 20 minutes of assembly time, while the Deluxe model requires 35 minutes of assembly time. The Standard model requires 10 minutes of inspection time, while the Deluxe model requires 15 minutes of inspection time. The company must fill an order for 6 Deluxe models. There are 450 minutes of assembly time and 180 minutes of inspection time available each day. How many units of each product should be manufactured to maximize profits? Answer: Maximum profit is $780 by producing 9 Standard and 6 Deluxe models.Diff: 3Topic: FORMULATING LP PROBLEMS and GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 81) Two advertising media are being considered for promotion of a product. Radio ads cost $400 each, while newspaper ads cost $600 each. The total budget is $7,200 per week. The total number of ads should be at least 15, with at least 2 of each type. Each newspaper ad reaches 6,000 people, while each radio ad reaches 2,000 people. The company wishes to reach as many people as possible while meeting all the constraints stated. How many ads of each type should be placed?Answer: Feasible corner points (R,N): (9,6) (13,2) (15,2)Maximum exposure 54,000 with 9 radio and 6 newspaper ads.Diff: 3Topic: FORMULATING LP PROBLEMS and GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 82) Suppose a linear programming (minimization) problem has been solved and the optimal value of the objective function is $300. Suppose an additional constraint is added to this problem. Explain how this might affect each of the following:(a) the feasible region,(b) the optimal value of the objective function.Answer:(a) Adding a new constraint will reduce the size of the feasible region unless it is a redundant constraint. It can never make the feasible region any larger. However, it could make the problem infeasible.(b) A new constraint can only reduce the size of the feasible region; therefore, the value of the objective function will either increase or remain the same. If the original solution is still feasible, it will remain the optimal solution.Diff: 2Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM and FOUR SPECIAL CASES IN LPAACSB: Analytic Skills 83) Upon retirement, Mr. Klaws started to make two types of children’s wooden toys in his shopWuns and Toos. Wuns yield a variable profit of $9 each and Toos have a contribution margin of $8 each. Even though his electric saw overheats, he can make 7 Wuns or 14 Toos each day. Since he doesn’t have equipment for drying the lacquer finish he puts on the toys, the drying operation limits him to 16 Wuns or 8 Toos per day. (a) Solve this problem using the corner point method.(b) For what profit ratios would the optimum solution remain the optimum solution?Answer: Corner points (0,0), (7,0), (0,8), (4,6)Optimum profit $84 at (4,6).Diff: 3Topic: FORMULATING LP PROBLEMS and GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 84) Susanna Nanna is the production manager for a furniture manufacturing company. The company produces tables (X) and chairs (Y). Each table generates a profit of $80 and requires 3 hours of assembly time and 4 hours of finishing time. Each chair generates $50 of profit and requires 3 hours of assembly time and 2 hours of finishing time. There are 360 hours of assembly time and 240 hours of finishing time available each month. The following linear programming problem represents this situation. Maximize 80X + 50YSubject to: 3X + 3Y ≤ 3604X + 2Y ≤ 240X, Y ≥ 0 The optimal solution is X = 0, and Y = 120. (a) What would the maximum possible profit be?(b) How many hours of assembly time would be used to maximize profit?(c) If a new constraint, 2X + 2Y ≤ 400, were added, what would happen to the maximum possible profit?Answer:(a) 6000, (b) 360, (c) It would not change.Diff: 3Topic: FORMULATING LP PROBLEMS and GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 85) As a supervisor of a production department, you must decide the daily production totals of a certain product that has two models, the Deluxe and the Special. The profit on the Deluxe model is $12 per unit, and the Special’s profit is $10. Each model goes through two phases in the production process, and there are only 100 hours available daily at the construction stage and only 80 hours available at the finishing and inspection stage. Each Deluxe model requires 20 minutes of construction time and 10 minutes of finishing and inspection time. Each Special model requires 15 minutes of construction time and 15 minutes of finishing and inspection time. The company has also decided that the Special model must comprise at most 60 percent of the production total. Formulate this as a linear programming problem.Answer:Diff: 2Topic: FORMULATING LP PROBLEMSAACSB: Analytic Skills 86) Determine where the following two constraints intersect.5X + 23Y ≤ 100010X + 26Y ≤ 1600Answer: (108, 20)Diff: 1Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 87) Determine where the following two constraints intersect.2X – 4Y = 800−X + 6Y ≥ -200Answer: (500, 50)Diff: 1Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 88) Two advertising media are being considered for promotion of a product. Radio ads cost $400 each, while newspaper ads cost $600 each. The total budget is $7,200 per week. The total number of ads should be at least 15, with at least 2 of each type, and there should be no more than 19 ads in total. The company does not want the number of newspaper ads to exceed the number of radio ads by more than 25 percent. Each newspaper ad reaches 6,000 people, 50 percent of whom will respond; while each radio ad reaches 2,000 people, 20 percent of whom will respond. The company wishes to reach as many respondents as possible while meeting all the constraints stated. Develop the appropriate LP model for determining the number of ads of each type that should be placed.Answer:Diff: 2Topic: FORMULATING LP PROBLEMSAACSB: Analytic Skills 89) Suppose a linear programming (maximization) problem has been solved and the optimal value of the objective function is $300. Suppose a constraint is removed from this problem. Explain how this might affect each of the following:(a) the feasible region.(b) the optimal value of the objective function.Answer:(a) Removing a constraint may, if the constraint is not redundant, increase the size of the feasible region. It can never make the feasible region any smaller. If the constraint was active in the solution, removing it will also result in a new optimal solution. However, removing an essential constraint could cause the problem to become unbounded.(b) Removal of a constraint can only increase or leave the same the size of the feasible region; therefore, the value of the objective function will either increase or remain the same, assuming the problem has not become unbounded.Diff: 2Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM and FOUR SPECIAL CASES IN LPAACSB: Analytic Skills 90) Consider the following constraints from a two-variable linear program. (1) X ≥ 0(2) Y ≥ 0(3) X + Y ≤ 50 If the optimal corner point lies at the intersection of constraints (2) and (3), what is the optimal solution (X, Y)?Answer: Y = 0, so X + 0 = 50, or X = 50. Thus the solution is (50, 0).Diff: 1Topic: GRAPHICAL SOLUTION TO AN LP PROBLEMAACSB: Analytic Skills 91) Consider a product mix problem, where the decision involves determining the optimal production levels for products X and Y. A unit of X requires 4 hours of labor in department 1 and 6 hours a labor in department 2. A unit of Y requires 3 hours of labor in department 1 and 8 hours of labor in department 2. Currently, 1000 hours of labor time are available in department 1, and 1200 hours of labor time are available in department 2. Furthermore, 400 additional hours of cross-trained workers are available to assign to either department (or split between both). Each unit of X sold returns a $50 profit, while each unit of Y sold returns a $60 profit. All units produced can be sold. Formulate this problem as a linear program. (Hint: Consider introducing other decision variables in addition to the production amounts for X and Y.)Answer: Maximize: 50X + 60YDiff: 3Topic: FORMULATING LP PROBLEMSAACSB: Analytic Skills92) A plastic parts supplier produces two types of plastic parts used for electronics. Type 1 requires 30 minutes of labor and 45 minutes of machine time. Type 2 requires 60 minutes of machine hours and 75 minutes of labor. There are 600 hours available per week of labor and 800 machine hours available. The demand for custom molds and plastic parts are identical. Type 1 has a profit margin of $25 a unit and Type 2 have a profit margin of $45 a unit. The plastic parts supplier must choose the quantity of Product A and Product B to produce which maximizes profit. (a) Formulate this as a linear programming problem.(b) Find the solution that gives the maximum profit using either QM for Windows or Excel.Answer: (b) X1 = 914.28, X2 = 114.28Diff: 2Topic: FORMULATING LP PROBLEMS and SOLVING FLAIR FURNITURE’S PROBLEM USING QM FOR WINDOWS and EXCELAACSB: Analytic Skills 93) A company can decide how many additional labor hours to acquire for a given week. Subcontractor workers will only work a maximum of 20 hours a week. The company must produce at least 200 units of product A, 300 units of product B, and 400 units of product C. In 1 hour of work, worker 1 can produce 15 units of product A, 10 units of product B, and 30 units of product C. Worker 2 can produce 5 units of product A, 20 units of product B, and 35 units of product C. Worker 3 can produce 20 units of product A, 15 units of product B, and 25 units of product C. Worker 1 demands a salary of $50/hr, worker 2 demands a salary of $40/hr, and worker 3 demands a salary of $45/hr. The company must choose how many hours they should contract with each worker to meet their production requirements and minimize labor cost. (a) Formulate this as a linear programming problem.(b) Find the optimal solution.Answer: (b) X1 = 0, X2 = 9.23, X3 = 7.69Diff: 3Topic: FORMULATING LP PROBLEMS and SOLVING FLAIR FURNITURE’S PROBLEM USING QM FOR WINDOWS and EXCELAACSB: Analytic Skills 94) Define dual price.Answer: The dual price for a constraint is the improvement in the objective function value that results from a one-unit increase in the right-hand side of the constraint.Diff: 2Topic: SENSITIVITY ANALYSIS 95) One basic assumption of linear programming is proportionality. Explain its need.Answer: Rates of consumption exist and are constant. For example, if the production of 1 unit requires 4 units of a resource, then if 10 units are produced, 40 units of the resource are required. A change in the variable value results in a proportional change in the objective function value.Diff: 2Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 96) One basic assumption of linear programming is divisibility. Explain its need.Answer: Solutions can have fractional values and need not be whole numbers. If fractional values would not make sense, then integer programming would be required.Diff: 2Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 97) Define infeasibility with respect to an LP solution.Answer: This occurs when there is no solution that can satisfy all constraints simultaneously.Diff: 2Topic: FOUR SPECIAL CASES IN LP 98) Define unboundedness with respect to an LP solution.Answer: This occurs when a linear program has no finite solution. The result implies that the formulation is missing one or more crucial constraints.Diff: 2Topic: FOUR SPECIAL CASES IN LP 99) Define alternate optimal solutions with respect to an LP solution.Answer: More than one optimal solution point exist because the objective function is parallel to a binding constraint.Diff: 2Topic: FOUR SPECIAL CASES IN LP 100) How does the case of alternate optimal solutions, as a special case in linear programming, compare to the two other special cases of infeasibility and unboundedness?Answer: With multiple alternate solutions, any of those answers is correct. In the other two cases, no single answer can be generated. Alternate solutions can occur when a problem is correctly formulated whereas the other two cases most likely have an incorrect formulation.Diff: 2Topic: FOUR SPECIAL CASES IN LPAACSB: Reflective Thinking