MANAGEMENT ADVISORY SERVICES
Quantitative Methods
Expected Value, Payoff Tables & Value of Perfect Information 1 . Gary’s Pipe and Steel Company expects sales next year to be P800,000 if the economy is strong, P500,000 if the economy is steady, and P350,000 if the economy is weak. Gary believes there is a 20 percent probability the economy will be strong, a 50 percent probability of a steady economy, and a 30 percent probability of a weak economy. What is the expected level of sales for next year?
Hotdogs self for P5.00 and cost Liberty P3 each. Unsold hotdogs are given to a local orphanage without charge. A. Construct a payoff table (conditional profits). B. What are the expected payoff of stocking 30,000 hotdogs and the expected value of perfect information? 4
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The Visitors Club sells brewed coffee at Araneta Gym's LBA's season games. The frequency distribution of the demand for cups of brewed coffee per game is presented below. Unit sales volume Probability 10,000 .10 20,000 .15 30,000 .25 40,000 .35 50,000 .15 The brewed coffee is sold for P1.00 a cup and the cost per cup is P0.25. Any unsold brewed coffee is discarded because it will spoil before the next home game. A. What is the estimated demand for brewed coffee at the next Araneta Gym's LBA's season game using an expected value approach? B. What is the estimated demand for brewed coffee at the next Araneta Gym's LBA's season game using a deterministic approach based on the most likely outcome? C. What is the conditional profit (loss) per game of having 25,000 cups of brewed coffee available but only selling 16,000 cups of coffee? Liberty, Inc. has been operating the concession stands at the university football stadium. The university has had successful football teams for many years; as a result the stadium is always full. The university is located in an area that suffers no rain during the football season. From time to time, Liberty has found itself very short of hotdogs and at other times it has had many left. A review of the records of sales of the past five seasons revealed the following frequency of hot dogs sold: Total Games 10,000 hot dogs 5 times 20,000 hot dogs 10 times 30,000 hot dogs 20 times 40,000 hot dogs 15 times 50 total games
Exercises & Problems
Gardenia Company makes corsages that it sells through salespeople on the streets. Each sells for P2 and has variable production costs of P0.80. The salespeople receive a P0.50 commission on each corsage they sell, and the company must spend P0.05 to get rid of each unsold corsage. The corsages last for only one week and cannot be carried in inventory. The manager of the firm had estimated demand per week and associated probabilities as follows: Demand Probability 100,000 0.20 120,000 0.20 140,000 0.30 160,000 0.30 A. What is the optimal weekly production of the corsage? B. What is the value of perfect information?
PERT-CPM 5 . The following are four series of activities with number of days to complete the different activities. I. A-B-D-F: 25, 18, 25, 14 II. A-B-E-F: 25, 18, 18,14 III. A-C-E-F: 25. 12, 18, 14 Required: A. Calculate the total time for each path, and identify the critical path. B. Which of the path(s) in the network can be delayed? What is(are) the activity(ies) that can be delayed and how many hours? C. How many slack days are there in Path III? D. What is the maximum number of days that can be applied to crash the critical path? 6
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The contractor is 2 days behind of completion of one of its multi-million projects. The daily penalty is P150,000 for any delay of completion time. The company has an opportunity of meeting the completion time if crashing is applied on the different activities. The PERT, which is not shown, indicated that the critical path is B-D-E-G-L. The following Page 1 of 7
MANAGEMENT ADVISORY SERVICES activities can be crashed at their respective costs: 1 day Activity A P135,000 Activity B 140,000 Activity C 125,000 Activity D 145,000 Activity E 155,000
Quantitative Methods
Required: 1. Which of the foregoing activity(ies) would be crashed? How much is the net benefit if the activity(ies) are crashed? 2. Assuming that the daily penalty is P140,000, which activities) will be crashed? Learning Curves 7 . Particular manufacturing job is subjected to an estimated 80% learning curve. The first unit required 100 labor hours to complete. REQUIRED: A. What is the cumulative average time per unit after 8 units are completed? B. What is the total time required to produce 2 units?; 4 units? C. How many hours are required to produce the second unit? 8
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manager believes that Leamwright could make the component with the following costs for the first batch of 1,000 units. Materials P130,000 Direct labor and variable overhead 150,000 Total variable cost P280,000 Making the component involves no incremental fixed costs because Learnwright could use existing equipment. The production manager expects an 85% learning rate on direct labor and variable overhead. Consider a batch to be 1,000 units. A. Determine whether Leamwright should make or buy the component. B. Assuming that the demand is a maximum of 16,000 units. Should Leamwright make or buy the component?
2days P260,000 285,000 240,000 295,000 280,000
Win Company manufactures large grape presses. The firm generally experiences a learning effect on new models, at least through the first 64 or so units. Data on a new press appear below: Labor time for first unit 500 hour Labor rate P500 per hour Variable overhead P10 per labor hour Materials P5,000 per press The manager of the firm wants to know the expected total cost of making the first 16 units, assuming a learning effect on labor of 90 percent. A. Prepare schedules showing the cumulative average time for all doubling points up through 16 units for a 90 percent learning rate. B. Determine the total costs for the first 16 units using a learning curve of 90 percent.
Learnwright Company currently buys at component for one of its products at P220 per unit. Leamwright needs 32,000 units of the component in the coming year. The product will be redesigned, so that the component will not be needed beyond the coming year. The production Exercises & Problems
Inventory Model 10 . I.M. Boring Company has projected sales of P72,000 pipes this year, an ordering cost of P6 per order, and carrying costs of P2.40 per pipe. A. What is the economic ordering quantity? B. How many orders will be placed during the year? C. What will the average inventory be? 11
. U.R. Terrific Company is trying to improve its inventory control system and has installed an online computer at its retail stores. It anticipates sales of 126,000 units per year, an ordering cost of P4 per order, and carrying costs of P1.008 per unit. A. What is the economic ordering quantity? B. What will be the average inventory be? C. What is the total cost of inventory expected to be? D. Assume a safety of stock of 30 units of inventory will be required as safety stock. What will be the new average inventory be? What will the new total carrying cost be?
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. Bayan Company uses 4,500 units of Part S-10 each year. The cost of placing one order of Part S-10 is estimated to be about P20. Other costs associated with carrying Part S-10 in inventory are: Annual Cost per Part Insurance P0.20 Property taxes 0.09 Interest on funds invested 0.15 Other 0.06 Total cost P0.50 A. Compute the economic order quantity (EOQ) for Part S-10. Page 2 of 7
MANAGEMENT ADVISORY SERVICES B. Assume that the company has been able to reduce the cost of placing an order to only P8. Also assume that when the waste and inefficiency caused by inventories is considered, the cost to carry a part in inventory jumps to P1.25 per unit. Under these conditions, what would be the EOQ? 13
. Flux Company uses 9,000 units of Part K each year. To get better control over its inventories, the company is anxious to determine the economic order quantity for this part. A. The company has determined that the cost to place an order for the part is P30, and it has determined that the cost to carry one part in inventory for one year is P1.50. Compute the EOQ for the part. B. Assume that the cost to place an order increases from P30 to P40 per order. What will be the effect on the EOQ? Show computations. C. Assume that the cost to carry a part in inventory increases from P1.50 to P2.50 per part. (Ordering costs remain unchanged at P30 per order.) What will be the effect on the EOQ? Show computations.
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. A company annually consumes 50,000 units of Part X. The carrying cost of this part is P3.00 per year and the ordering costs are P200. The company uses an order quantity of 5,000 units. Based on the information, compute: A. Average number of inventory units. B. Number of orders per year. C. Using 360 days a year, the frequency of making an order. D. The annual inventory costs, broken down into ordering and carrying costs. E. The economic order quantity. Compute the amount of annual inventory costs if the company uses the economic order quantity.
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. Delma Company distributes medical supplies throughout the country. Selected information relating to a quick-developing X-ray film carried by the company is given below: Economic order quantity (EOQ) 700 units, Maximum weekly usage 60 units Lead time 4 weeks Average weekly usage 50 units Management is trying to determine the proper safety stock to carry on this inventory item and to determine the proper reorder point. A. Assume that no safety stock is to be carried. What is the reorder point? B. Assume that a full safety stock is to be carried. 1. What would be the size of the safety stock in units?
Exercises & Problems
Quantitative Methods 2. What would be the reorder point? 16
. Ibon Company uses a small casting in one of its finished products. The castings are purchased from a foundry located in another Asian country. In total, Ibon Company purchases 54,000 castings per year at a cost of P8 per casting. The castings are used evenly throughout the year in the production process on a 360-day-peryear basis. The company estimates that it costs P90 to place a single purchase order and about P3 to carry one casting in inventory for a year. The high carrying costs result from the need to keep the castings in carefully controlled temperature and humidity conditions, and from the high cot of insurance. Delivery from the foundry generally takes 6 days, but it can take as much as 10 days. The days of delivery time and the percentage of their occurrence are shown in the following tabulation: Delivery Time (days) Percentage of Occurrence 6 75 7 10 8 5 9 5 10 5 100 A. Compute the economic order quantity (EOQ). B. Assume that the company is willing to assume a 15% risk of being out of stock. What would be the safety stock? The reorder point? C. Assume that the company is willing to assume only a 5% risk of being out of stock. What would be the safety stock? The reorder point? D. Assume a 5% stock-out risk as stated in (3) above. What would be the total cost of ordering and carrying inventory for one year? E. Refer to the original data. Assume that using process reengineering the company reduces its cost of placing a purchase order to only P6. Also, the company estimates that when the waste and inefficiency caused by inventories are considered, the true cost of carrying a unit in stock is P7.20 per year. Required: A. Compute the new EOQ. B. How frequently would the company be placing an order, as compared to the old purchasing policy?
Multiple Choice Page 3 of 7
MANAGEMENT ADVISORY SERVICES 3. A company is designing a new regional distribution warehouse. To minimize delays in loading and unloading trucks, an adequate number of loading docks must be built. The most relevant technique to assist in determining the proper number of docks is A. linear programming C. queuing theory B. PERT/CPM analysis D. correlation and regression analysis 14. Clay Co. operates three shipping terminals, referred to as X, Y, and Z. Of the total cargo shipped, terminals X, Y, and Z handle approximately 60%, 30%, and 10%, respectively, with error rates of 3%, 4%, and 6%, respectively. Clay's internal auditor randomly selects one shipping document, ascertaining that this document contains an error. The probability that the error occurred in terminal X is A. 60% C. 23% B. 50% D. 3% 4. Bye Co. is considering the sale of banners at the state university football championship game. Bye could purchase these banners for P.60 each. Unsold banners would be unreturnable and worthless after the game. Bye would have to rent a booth at the stadium for P250. Bye estimates sales of 500 banners at P2.00 each. If Bye’s prediction proves to be incorrect and only 300 banners were sold, the cost of this prediction error would be A. P120 C. P170 B. P130 D. P280 5. A wine maker must decide whether to harvest grapes now or in four weeks. Harvesting now will yield 100,000 bottles of wine netting P2 per bottle. If the wine maker waits and the weather turns cold (probability 0.2), the yield will be cut in half but net P3 per bottle. If the weather does not turn cold, the yield will depend on rain. With rain (probability 0.5), a full yield netting P4 per bottle will result. Without rain (probability 0.5), there will still be a full 100,000-bottle yield, but the net will be only P3 per bottle. The optimal expected value is A. P200,000 C. P350,000 B. P310,000 D. P400,000 8. The Polly Company wishes to determine the amount of safety stock that it should maintain for Product D that will result in the lowest cost. The following information is available: Stockout cost P80 per occurrence Carrying cost of safety stock P2 per unit Number of purchase orders 5 per year The options available to Polly are as follows: Exercises & Problems
Quantitative Methods Units of safety stock Probability of Running out of safety stock 10 50% 20 40% 30 30% 40 20% 50 10% 55 5% The number of units of safety stock that will result in the lowest cost is A. 20 C. 50 B. 40 D. 55 9. The following data refer to various annual costs relating to the inventory of a single-product company: Unit Transportation-in on purchases P0.20 Storage per unit 0.12 Insurance per unit 0.10 Annual interest foregone from alternate investment of funds P800 Annual number of units required 10,000 What is the annual interest cost per unit? A. P0.22 C. P0.42 B. P0.30 D. P0.50 10. Happy Holidays produces three products: X, Y, and Z. Two machines are used to produce the products. The contribution margin, sales demand, and time on each machine (in minutes) is as follows: Demand CM Time on M1 Time on M2 X 100 P10 5 10 Y 80 18 10 5 Z 100 25 15 5 There are 2,400 minutes available on each machine during the week. How many units should be produced and sold to maximize the weekly contribution? A. B. C. D. X 100 20 100 100 Y 80 80 40 80 Z 100 100 100 73 11. Ridgefield, Inc. is considering a three-phase research project. The time estimates for Page 4 of 7
MANAGEMENT ADVISORY SERVICES completion of phase 1 of the project are Optimistic 4 months Most likely 8 months Pessimistic 18 months Using the program evaluation and review technique (PERT), the expected time for completion of phase 1 should be A. 8 months C. 10 months B. 9 months D. 18 months
Quantitative Methods Solution
12. Wind Company expects an 85% learning curve. The first batch of a new product required 500 hours. The first four batches should take an average of A. 361.25 hours C. 500.0 hours B. 425.0 hours D. 322.4 hours 13. Havenot has estimated the first batch of product will take 40 hours to complete. A 90% learning curve is expected. If labor is paid P15 per hour, the target labor cost for four batches of product is A. P600 C. P1,944 B. P2,160 D. P2,400 14. Hanip Co. used 30 hour to produce the first batch of units. The second batch took an additional 18 hours. How many total hours will the first four batches require? A. 76.8 hours C. 120.0 hours B. 96.2 hours D. 48.0 hours 15. Moss Company recently completed and sold an order of 50 units that had the following costs: Direct materials P 1,500 Direct labor (1,000 hours @ P8.50) 8,500 Variable overhead (1,000 hours @ P4.00)* 4,000 Fixed overhead** 1,400 Total P15,400 * Applied on the basis of direct labor hours **Applied at the rate of 10 percent of variable cost The company has now been requested to prepare a bid for 150 units of the same product. If an 80 percent learning curve is applicable, Moss Company's total cost on this order would be estimated at A. P26,400 C. P37,950 B. P31,790 D. P37,500 Exercises & Problems
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. (A) (B) 40,000 (C) 9,750
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515,000 (800,000 X 20% + 500,000 X 50% + 350,000 X 30%)
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33,000
10,000 x 0.10 + 20,000 x 0.15 + 30,000 x 025 + 40,000 x 0.35 + 50,000 x 0.15
(16,000 x 1) – (25,000 x 0.25)
(A)
Probability10%20%40%30%Exp. ValueSup/Dem10,00020,00030,00040,00010,00020,00020,00020,00020,00020,00020,000(10,000)40,00040,00040,000 35,00030,000(40,000)10,00060,00060,00040,00040,000(70,000)(20,000)30,00080,00025,000(B) 58,000 Value at certainty 40,000 Highest expected value 18,000 Value of perfect information. 4
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. (B) (C) (D)
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. (1) E – 2 days (280,000) (2) B – 1 day (140,000), or E for 2 days = P280,000
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124816Cum. ave. time100806451.240.96Cum. time160256409.6655.36Incremental time6096153.6245.76 . (A) 5,248.8 (500 X 0.9 X 0.9 X 0.9 X 0.9 = 328.05 X 16) (B) 2,756,888 (5,248.8 x 510) + (5,000 x 16)
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Payoff Table Probability0.200.200.300.30Expected ValueSup/Dem100,000120,000140,000160,000100,00070,00070,00070,000 70,00070,000120,00053,00084,00084,000 84,00077,800140,00036,00067,00098,000 98,00079,400160,00019,00050,00081,000112,00071,700(B) 14,400 Value of perfect information = (93,800 – 79,400) (A) A-B-D-F = 82, A-B-E-F = 75, A-C-E-F = 69, Critical path A-B-D-F Paths E can be delayed for a max. of 7 days and C & E for a max. of 13 days Slack days = 82 – 69 = 13. maximum crash days = 7 (82 – 75)
(A) DL & VOH Materials Total Unit Cost
Make 1,252,815 2,080,000 3,332,815 208.30
(B) Make DL & VOH Materials Total Unit cost
2,129,785 4,160,000 6,289,785 196,56
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. (A) (B) 120 (C) 300
600
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. (A) (B) 500 (C) 504
1,000
(150,000 x 85% x 85% x 85% x 85% = 78,300.94 x 16) (130,000 x 16)
(150,000x 85% x 85% x 85% x 85% x 85%= 78,300.94 x 32) (130,000 x 32)
(D) 530 534.24 (530 X 1.008) 12
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(A)
(B) 240
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(A)
(B) 692.83 (C) 464.76 14
. (B) (C) (D)
1.25
16
. (B) (C) (D)
(E1)
2(9,000)(30)
600
1.50
2(9,000)(40) 1.50 2(9,000)(30) 2.50
(A) 10 Every 36 days 9,500
7,746 . (B1) (B2)
0.50
2(4,500)(8)
(E) EOQ = 2,582
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2(4,500)20
600
2,500 (5,000 2) (50,000 5,000) (360 10) Ordering cost = 2,000 (200 x 10), Carrying Cost = 7,500 (2,500 x 3) 2(50,000)200 3 Ordering cost = 3,873 (19.36 x 200), Carrying Cost = (3,873) 1291 x 3
(A) 40 240 (A)
200 (50 X 4) (10 X 4) (60 X 4) or (50 x 4) + 40
1,800 150 1,050 450 1,350 2,700 4,050 6,750 300
(E2) every 2 days
2(54,000)90 3
360) x 1 360) x 7 360) x 3 360) x 9
(54,000 (54,000 (54,000 (54,000 Ordering cost (54,000 1,800) x 90 Carrying cost [(1,800 2) + 450] x 3 Total Cost of ordering& carrying
2(54,000)6 7.20 (54,000 300) = 180 times a year.
