E. QUANTITATIVE METHODS THEORIES:
Economic Order Quantity
1. The economic order quantity is the order quantity that results in A. the minimum total annual inventory costs.
B. no inventory shortages.
C. the maximum total annual inventory costs. D. minimum ordering costs.
Sensitivity analysis
2. Missile Company has correctly computed its economic order quantity as 500 units. However, management feels it would rather order quantities of 600 units. How should Missile’s total annual purchase-order costs and total annual carrying cost for an order quantity of 600 units compare to the respective amounts for an order quantity of 500 units?
A. Higher purchase-order cost and lower carrying cost. B. Higher purchase-order cost and higher carrying cost. C. Lower purchase-order cost and higher carrying cost. D. Lower purchase-order cost and lower carrying cost. 3. A decrease in inventory order costs will
A. Increase the reorder point.
B. Decrease the economic order quantity. C. Have no effect on the economic order quantity. D. Decrease the holding cost percentage. 4. An increase in inventory holding costs will
A. Decrease the economic order quantity. B. Have no effect on the economic order quantity. C. Increase the economic order quantity.
D. Decrease the number of orders issued per year. PERT-CPM
5. Which one of the following statements best describes a difference between basic PERT and the Critical Path Method (CPM) of network analysis?
A. PERT uses probability distribution on the activity times while CPM uses point estimates
for the activity times.
B. PERT does not allow for slack times on the activities while CPM does. C. PERT considers only activity cost while CPM considers only activity time.
D. PERT determines the cost path through a network while CPM determines the least-time path through a network.
6. Critical Path Method (CPM) is a technique for analyzing, planning, and scheduling large, complex projects by determining the critical path from a single time estimate for each event in a project. The critical path:
A. Is the shortest path from the first event to the last event for a project. B. Is an activity within the path that requires the most number of time. C. Has completion that reflects the earliest time to complete the project.
D. Is the maximum amount of time an activity may be delayed without delaying the total project beyond its target completion time.
Queuing Theory
7. 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 docks is
A. Cost-volume-profit analysis C. Linear programming B. PERT/CPM analysis D. Queuing theory Linear Programming
Use the following information to answer question Nos. 8 and 9:
The Kinis Company produces a cosmetic product in 60 gallon batches. The basic ingredients used are material X, costing P70 per gallon, and material Y, costing P170 per gallon. No more than 18 gallons of X can be used, and at least 15 gallons of Y must be used.
8. How would the objective function (minimization of product cost) be expressed?
A. 70X + 170Y C. 170X + 70Y
B. 18X + 15Y D. 18X + 42Y
9. Which of the following is not a constraint of the Kinis Company?
A. X ≤ 18 C. Y ≥ 15
B. X + Y ≤ 60 D. X ≥ 0
Sun, Inc. manufactures product X and product Y, which are processed as follows: Type A machine Type B machine
Product X 6 hours 4 hours
Product Y 9 hours 5 hours
The contribution margin is P12 for product X and P7 for product Y. The available time daily for processing the two products is 120 hours for machine Type A and 80 hours for machine Type B. 10. How would the constraint for machine Type A be expressed?
A. 4X + 5Y C. 4X + 5Y ≤ 80
B. 6X + 9Y ≤ 120 D. 12X + 7Y
11. How would the constraint for machine Type B be expressed?
A. 4X + 5Y C. 4X + 5Y ≤ 80
B. 6X + 9Y ≤ 120 D. 12X + 7Y
12. How would the objective function be expressed?
A. 4X + 5Y C. 4X + 5Y ≤ 80
B. 6X + 9Y ≤ 120 D. 12X + 7Y
PROBLEMS: PERT-CPM
2. Castle Building Company uses the critical path method to monitor construction jobs. The company is currently 2 weeks behind schedule on Job WW, which is subject to a P10,500-per-week completion penalty. Path A-B-C-F-G-H-I has a normal completion time of 20 P10,500-per-weeks, and critical path A-D-E-F-G-H-I has a normal completion time of 22 weeks. The following activities can be crashed.
Activities Cost to Crash 1 Week Cost to Crash 2 Weeks
BC P 8,000 P15,000
DE 10,000 19,600
EF 8,800 19,500
Castle desires to reduce the normal completion time of Job WW and, at the same time, report the highest possible income for the year. Castle should crash
A. Activity BC 1 week and activity EF 1 week B. Activity BC 2 weeks
C. Activity DE 1 week and activity BC 1 week D. Activity DE 1 week and activity EF 1 week Learning Curve
1. Contratista, Inc. is considering a three-phase research project. The time estimates for
completion of Phase 2 of the project are:
Pessimistic 24 weeks
Most likely 20 weeks
Optimistic 10 weeks
Using the program evaluation and review technique (PERT), the expected time for completion of Phase 2 should be
A. 20 weeks C. 18 weeks
B. 19 weeks D. 24 weeks
2. 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
3. A learning curve of 80% assumes that production unit costs are reduced by 20% for each
doubling of output. What is the cost of the sixteenth unit produced as an approximate percent of the first unit produced?
A. 30 percent C. 41 percent
B. 51 percent D. 64 percent
4. Soft Inc. has a target total labor cost of P3,600 for the first four batches of a product. Labor
is paid P10 an hour. If Soft expects an 80% learning curve, how many hours should the first batch take?
A. 360 hours C. 57.6 hours
B. 140.63 hours D. 230.4 hours
5. 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
6. Hanip Co. used 30 hours 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
7. Sulit Company plans to begin production of a new product on July 1. An 80% learning curve is
applicable to Sulit’s manufacturing operations. If it is expected to take 1,000 direct labor hours to produce the first unit, how many direct labor hours should it take to produce the third and fourth units?
A. 640 C. 1,600
B. 960 D. 2,560
8. A construction company has just completed a bridge over the Visayan area. This the first
bridge the company ever built and it required 100 weeks to complete. Now having hired a bridge construction crew with some experience, the company would like to continue building bridges. Because of the investment in heavy machinery needed continuously by this crew, the company believes it would have to bring the average construction time to less than one year (52 weeks) per bridge to earn a sufficient return on investment. The average construction time will follow an 80% learning curve. To bring the average construction time (over all bridges constructed) below one year per bridge, the crew would have to build approximately
A. 2 additional bridges. C. 3 additional bridges. B. 7 additional bridges. D. 8 additional bridges.
9. Moss Point Manufacturing 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 at P4.00) 4,000
Fixed overhead 1,400
P15,400 *Applied on the basis of direct labor hours.
*Applied at the rate of 10% 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 Point’s total cost on this order would be estimated at
A. P26,400 C. P31,790
B. P37,950 D. P38,500
Expected Value
10. Dough Distributors has decided to increase its daily muffin purchases by 100 boxes. A box of
muffins costs P2 and sells for P3 through regular stores. Any boxes not sold through regular stores are sold through Dough’s thrift store for P1. Dough assigns the following probabilities to selling additional boxes:
Additional sales Probability
60 0.6
100 0.4
What is the expected value of Dough’s decision to buy 100 additional boxes of muffins?
A. P28 C. P52
B. P40 D. P68
11. Karen Company has three sales departments. Department A processes about 50 percent of
sales, Department B about 30 percent, and Department C about 20 percent. In the past, Departments A, B, and C had error rates of about 2 percent, 5 percent, and 2.5 percent, respectively. A random audit of the sales records yields a recording error of sufficient magnitude to distort the company’s results. The probability that Department A is responsible for this error is
A. 0.50 C. 0.20
B. 0.33 D. 0.25
12. A beverage stand can sell either softdrinks or coffee on any given day. If the stand sells
softdrinks and the weather is hot, it will make P2,500; if the weather is cold, the profit will be P1,000. If the stand sells coffee and the weather is hot, it will make P1,900; if the weather is cold, the profit will be P2,000. The probability of cold weather on a given day at this time is 60%. The expected payoff if the vendor has perfect information is
A. P3,900 C. P2,200
B. P1,360 D. P1,960
13. The Teeners’ Club sells fresh hot cider at Recto football games. The frequency distribution
of the demand for cups of hot cider per game is presented below:
Unit sales volume Probability
10,000 0.10
20,000 0.15
40,000 0.40
50,000 0.20
The hot cider is sold for P35.00 a cup and the cost per cup is P20.00. Any unsold hot cider is discarded because it will spoil before the next game.
What is the estimated demand for hot cider at the next football game if a deterministic approach based on the most likely outcome is used?
A. 34,500 C. 16,000
B. 40,000 D. 50,000
14. Green Co. is considering the sale of banners in an exhibit fair. Green Co. could purchase
these banners for P7.50 each. Unsold banners would be unreturnable and worthless after the exhibit. Green would have to rent a booth at the stadium for P4,000. Green estimates sales of 2,000 banners at P20.00 each. If Green’s prediction proves to be incorrect and only 1,500 banners were sold, the cost of this prediction error would be:
A. P 6,250 C. P 4,750
B. P10,000 D. P 3,750
15. The manager of Batanes Company has developed the following probability distribution of
dairy sales of a highly perishable product. The company restocks the product each morning:
X (Units Sold P (Sales =X)
150 0.20 175 0.40 200 0.15 225 0.10 250 0.10 275 0.05
If the company desires an 85% service level in satisfying sales demand, what should the initial balance be for each day?
A. 191 C. 234
B. 225 D. 250
Question Nos. 17 and 18 are based on the following:
Sampaguita 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
16. The optimal weekly production of the corsage is
A. 120,000 C. 134,000
B. 140,000 D. 145,000
17. The value of perfect information is
A. P14,400 C. P23,800
B. P16,000 D. P22,100
Question Nos. 21 through 24 re based on the following information:
Glassco, Inc. has two products, a frozen dessert and ready-to-bake breakfast rolls, ready for introduction. However, plant capacity is limited, and only one product can be introduced at present. Therefore, Glassco has conducted a market study, at a cost of P26,000, to determine which product will be more profitable. The results of the study show the following sales patterns.
Sales of Desserts at P1.80 per unit Sales of Rolls at P1.20 per unit
Volume Probability Volume Probability
250,000 .30 200,000 .20
300,000 .40 250,000 .50
350,000 .20 300,000 .20
400,000 .10 350,000 .10
The costs associated with the two products have been estimated by Glassco’s cost accounting department and are shown below:
Dessert Rolls
Ingredients per unit P 0.40 P 0.25 Direct labor per unit 0.35 0.30 Variable overhead per unit 0.40 0.20
Production tooling* 48,000.00 25,000.00
*Glassco treats production tooling as a current operating expense rather than capitalizing it as a fixed asset.
18. According to Glassco’s market study, the expected value of the sales volume of the breakfast
rolls is
A. 125,000 units C. 260,000 units
B. 275,000 units D. 250,000 units
19. Applying a deterministic approach, Glassco’s revenue from sales of frozen desserts would be
A. P549,000 C. P540,000
B. P195,000 D. P216,000
20. The expected value of Glassco’s operating profit directly traceable to the sale of frozen
desserts is
A. P198,250 C. P471,000
B. P150,250 D. P120,250
21. In order to recover the costs of production tooling and advertising for the breakfast rolls,
Glassco’s sales of the breakfast rolls would have to be
A. 37,500 units C. 100,000 units
B. 60,000 units D. 54,000 units
Decision Tree
22. 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 100,000-bottle.
The optimal expected value is
A. P200,000 C. P350,000
B. P310,000 D. P400,000
Theory of Constraints
23. Happy Holidays produces three products: X, Y, and Z. Two machines are used to produce the
products. The contribution margins, sales demands, 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 maximize the weekly contribution?
X Y Z A. 100 80 100 B. 20 80 100 C. 100 40 100 D. 100 80 73 Inventory Management
EOQ, Safety Stock, Reorder Point
Question Nos. 25 through 30 are based on the following:
KMU 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, KMU 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-per-year 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. 1,800 C. 2,545
B. 1273 D. 2,700
25. Assuming that the company will not provide any safety stock units, how much would the
annual inventory costs?
A. P2,700 C. P5,400
B. P8,100 D. P6,000
26. Assuming that the company is willing to assume a 15% risk of being out of stock, what would
be the number of safety stock?
A. 0 C. 300
B. 150 D. 450
27. Assuming that the company is willing to assume only a 5% risk of being out of stock, what
would be the reorder point?
A. 450 C. 1,200
B. 1,050 D. 1,350
28. Assuming a 5% stock-out risk, what would be the total cost of ordering and carrying inventory
for one year?
A. 5,850 C. 6,075
B. 6,300 D. 6,750
29. Assuming that the cost of stock out is P800 per occurrence, which safety stock level is
necessary in reducing the cost?
A. 0 C. 300
B. 150 D. 450
Just-in-Time
30. At the beginning of 2007, Silang Company installed a JIT purchasing and manufacturing
system. The following information has been gathered about one of the company's products
Theoretical annual capacity 4,000
Actual production 3,800
Production hours available 2,500
On-time deliveries 1,500
Total deliveries 1,600
Scrap (lbs.) 400
Materials used (lbs.) 12,800
Number of defective units 20
Defective units as a percentage of total units produced is:
A. 5% C. 0.53%
B. 1.05% D. 2.5%
2 . Answer: A
UnitsCumulative Average TimeComputation1500.002425.00(0.85 x 500.00)4361.25(0.85 x 425.00)
3 . Answer: C
UnitsCumulative Average TimeComputation11.0020.80(0.8 x 1.00)40.64(0.8 x 0.80)80.51(0.8 x 0.64)160.41(0.8 x 0.51)Percentage: 0.41 ÷1.00 = 41.0%
4 . Answer: B
Average hours after 4th batch P3,600 ÷ 10 ÷ 4 units 90
Hours used by 1st batch: 90 ÷ 0.80 ÷ 0.80 140.63 5 . Answer: C
UnitsCumulative Average TimeComputation140.00236.00(0.9 x 40.00)432.40(0.9 x 36.00)
Total number ofhours used by 4 units: 4 x 32.4 129.6
Total labor cost used by 4 units: 129.6 x P15 P1,944
6 . Answer: A
Learning curve (30 + 18) ÷ 2 ÷ 30 = 80.0% Cumulative average time after 4 batches: 30 x 0.8 x 0.8 19.2 Total number of hours used by first 4 batches: 4 x 19.2 76.8
7 . Answer: B
Cumulative average DLH after 4 units: (1,000 x 0.8 x 0.8) 640 Total DLH after 4 units: 4 x 640 2,560 Less Total DLH used after 2 units (1,000 x 0.8 x 2) 1,600 Total DLH used by 3rd and 4th units 960 8 . Answer: B
No. of BridgesCumulative Average WeeksComputation1100.00280.00(0.8 x 100.0)464.00(0.8 x
80.00)851.20(0.8 x 64.00)
It will take 8 bridges to complete them with cumulative average time in weeks of below 52. The company needs to complete additional 7 bridges to have an average completion time of less than 52 weeks.9 . Answer: A
Cumulative Ave. DHL50 units20.0100 units16.0( 20 x 80% )200 units12.80( 16 x 80% )Total hrs required by 200
units 128.80 x 2,000 2,560
Less Hours used by first 50 units 1,000
Additional Hours 1,560
Costs
Direct materials (1,500 x 3) P 4,500
Direct labor 1,560 x 8.50 13,260
Variable OH 1,560 x 4 6,240
Total variable Costs 24,000 Fixed OH 10% x 24,000 2,400
Total Cost P26,400
10 . Answer: C
Dept.ErrorWeightProbabilityA0.020.010.01/.03 = 33.00%B0.050.015.015/03= 50.00% C0.0250.05.005/03= 16.67%0.03
12 . Answer: C
Expected payoff:
Sale of coffee during cold weather 2,000 x 0.6 1,200 Sale of soft drinks during hot weather 2,500 x 0.4 1,000
Total 2,200
13 . Answer: B
The expected sales based on the most likely outcome are 40,000. This is based on the concept that which one with the highest probability is the most likely to happen.
14 . Answer: D
The cost of prediction error = unsold units x purchase price 500 x 7.50 = P3,750
15 . Answer: B
At the service level of 85%, there is 15% risk that the company runs out of stock. To achieve 85% level, 225 units must be purchased at the start of day. (0.20 + 0.40 + 0.15 + 0.10 = 85%); 225 units corresponds to 85%.
16 . Answer: B
PurchasesProbabilityDemand100,000120,000140,000160,000 20%100,00070,00053,00036,000 19,00020%120,00070,00084,00067,000 50,00030%140,00070,00084,00098,000 81,00030%160,00070,00084,00098,000112,000Expected Value 70,000 77,800 79,400 71,700Optimal Production is 140,000 because it gives the highest pay off, which is 79,400
17 . Answer: A
Perfect Information:
(70,000 x.20) + (84,000 x .20) + (98,000 x.3) + (112,000 x .30) = 93,800 Value of Perfect Info – 93,800 – 79,400 = P14,400
Value of Perfect Info = Diff. Between payoff of Perfect Info and Optimal production
18 . Answer: C
EV = (200 x 0.2) + (250 x 0.5) + (300 x 0.2) + (350 x 0.1) 60,000
19 . Answer: C
300,000 x P1.80 = P540,000
The sales level of 300,000 has the highest probability (40%) and there it the level most likely to happen.
20 . Answer: D
EV: (250 x 0.3) + (300 x 0.4) + (350 x 0.2) + (400 x 0.1) 305,000
Expected sales (305,000 x P1.80) P549,000
Less expected variable costs (305,000 x P1.15) 350,750
Contribution margin 198,250
Less fixed costs (P48,000 + P30,000) 78,000
Expected profit P120,250
Expected value if immediately harvested: (100,000 x P2) P200,000 Expected value if not harvested immediately:
Cold weather: (50,000 x P3 x 0.20) P 30,000 Not cold with rain: (100,000 x P4 x 0.8 x 0.5) 160,000 Not cold without rain: (100,000 x P3 x 0.8 x. 0.5) 120,000
Total P310,000
23 . Answer: D
First step is to determine which machine has a constraint: Required usage of Machine:
Machine 1: (100 x 5) + (80 x 10) + (100 x 15) 2,800 Machine 2: (100 x 10) + (80 x 5) + (100 x 5) 1,900 Machine 1 has shortage in capacity of (2,800 – 2,400) 400
Second step is to determine the order of profitability of the product lines per minute of machine 1.
Product X: P10 ÷ 5 min. P2.00
Product Y: P18 ÷ 10 min. 1.80
Product Z: P25 ÷ 15 min. 1.67
The company should produce product Z last because it is the least profitable per minute of usage of Machine 1. It is apparent that Choice D is the only possible correct response.
24 . Answer: A
EOQ = the square root of 2 x annual units required x ordering cost ÷ carrying cost per unit EOQ = the square root of 2 x 54,000 x 90,000 ÷ 3 = 1,800
25 . Answer: C
Annual ordering cost: 54,000/1800 x 90 2,700
Annual carrying cost: 1,800/2 x 3 2,700
Total cost 5,400
26 . Answer: B
A 15% risk of out-of-stock means a 85% assurance that order will be received on time. Without having a safety stock, the company will use a lead time of 6 days (75%). Therefore, 7-day lead time has 85% assurance or a 15% risk of stockout. The safety stock level is for 1 day (7 – 6) or 150 units.
Daily requirements: 54,000/360 = 150
27 . Answer: D
A 5% risk of out-of-stock means a 95% assurance that order will be received on time. This is estimated to have a lead time of 9 days (the total of probability for 9 days is 95%).
Reorder point without safety stock 6 days x 150 900
Safety stock (9 – 6) 150 450
Reorder point 1,350
28 . Answer: D
Ordering cost (unchanged) 2,700
Carrying cost
Average inventory (1800/2) + 450 = 1,350
Safety unitsStock out costCarrying CostTotal 00.25 x 2,400 = 600 0 6001500.15 x 2,400 = 360150 x 3 = 450 8103000.10 x 2,400 = 240300 x 3 = 9001,1404500.05 x 2,400 = 120450 x 3 = ,3501,470Annual stockout
cost (100% probability) based 30 orders (54,000/1800): 30 x 800 = 2,400
The probability of stockout is the inverse of assurance, say at zero safety stock, 6 days, its 75% probable that ordered goods will arrive, therefore, its 25% probable that it won’t.
30 . Answer: C
