# Management Science

Posttest – Posttest

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Question 1. 1. Tippalee Ventures Inc. provides helicopter tours of the wilderness. The fixed monthly cost for the helicopter, gear, and

airport space is $42,500. The variable cost per tour is $6,500. The helicopter tours sell for $3,500 per person, and the helicopter seats

three customers. Assuming every helicopter is filled to capacity, what is the break-even volume for the company? What is the break-even

volume if each helicopter only carries two customers? (Points : 4)

Question 2. 2. A model in management science is: (Points : 2)

a previously unknown problem.

a symbol representing a numeric value.

a graph or chart.

an abstract representation of an existing problem situation.

a small-scale recreation of a factory or warehouse.

Question 3. 3. Gold Star Delicacies makes small-batch jams and jellies. Their workspace and equipment cost them $2600 per month in loans,

and operating costs total an additional $700 per week. The variable cost per batch of jam in materials and labor is $350. Each batch can

fill 200 bottles and each bottle can sell for $3.75. Find the break-even point for how many batches of jam they must sell in a month,

assuming they sell all the bottles from each batch produced. What happens to the break-even point if 8% of the bottles from each batch are

wasted and cannot be sold? What happens to the original break-even point if, instead, costs per batch go up by another $75? (Points : 3)

Question 4. 4. Gregory’s company has ordered a large supply of paint, but the manufacturer says there is a possibility that the batch they

received was defective. However, the company has no choice but to start filling orders, and they are trying to decide where they can

safely use the paint. They estimate their profits based on expected rates of return for different products if the paint fails.

Product Paint is not defective Paint is defective

Table/chairs $16,600 $350

Cabinets $35,450 -$4,750

Fixtures $18,450 -$750

Dressers $22,000 -$2,050

(Points : 3)

Question 5. 5. Should Vulco Rubber Inc. invest in a new production plant? Evaluate the payoff table below using the maximax, maximin, and

minimax regret criteria.

Decision Economy improves Economy worsens

Invest in Plant A $140,000 -$30,000

Invest in Plant B $260,000 -$95,000

Do not invest $32,000 $24,000

(Points : 4)

Question 6. 6. Delicatessen Catering Co. provides catering services for weddings, reunions, business functions, and a variety of other

social events. Delicatessen is thinking of hiring more staff to keep up with rising demand. This would require purchasing more equipment

and vehicles to ensure these staff can do their jobs. Determine what choice they should make using the Hurwicz (α = 0.7 and α = 0.4) and

equal likelihood criteria. What are the expected values?

Decision Increased demand Decreased demand

Hire staff $25,040 -$18,950

Do not hire $5,650 $4,970

(Points : 4)

Question 7. 7. Home Furnishings and Decorations Inc. can revamp the loading area of their warehouse to improve the efficiency of loading

trucks. They have two possible proposals for the work, one that modernizes their current setup and one that is a new layout, which would

be a sweeping change in workflow but promises a huge gain in efficiency for high volumes of traffic. The new layout, however, is a lot

more expensive to build. Use the payoff table to determine the expected profit or loss for each purchase, and determine the optimal

purchase.

Plan Gain clients (0.4) No change (0.4) Lose clients (0.2)

New loading layout $32,400 $5,250 -$45,450

Modernized layout $12,290 $10,050 -$10,800

No change $9,400 $0 -$2,600

(Points : 5)

Question 8. 8. Green Thumb Garden Supply orders plants to sell to its customers. Each plant costs $23 to purchase and another $15 to grow

and feed for the season. The plants will be sold for $65 a piece. Once the season is over, the remaining plants will be sold for just $25.

The company estimates demand for the plants in the table below. Generate a payoff table, and compute the expected value for each

alternative. What is the expected value for perfect information? How many plants should the garden supply company purchase?

Demand Probability

22 0.15

23 0.25

24 0.25

25 0.25

26 0.10 (Points : 8)

Question 9. 9. Howard American Cycles makes and sells custom motorcycles, and does modifications on customers’ motorcycles. So far most of

their advertising is done through word-of-mouth. The cycle manufacturer has decided to start advertising through other methods over the

next few months. They are choosing between different advertising avenues, and have hired a firm to do market research and estimate the

profitability of each choice. Using the information below, create a decision tree for Howard American Cycles and compute the expected

value of each advertising avenue. How should Howard American Cycles advertise its product?

Advertising Economy improves (0.25) Stable (0.5) Falls (0.25)

Print $8,240 $3,120 $800

Web $9,514 $7,650 $4,310

TV $23,900 $10,400 -$18,680

Radio $12,010 $8,050 $1,200

(Points : 5)

Question 10. 10. Delaware Coffee Roasters, LLC. is considering moving its coffee roasting operation from the back of the store to some

neighboring warehouse space. The company has to decide how much space to rent and how to handle sales and distribution. They make a payoff

table, shown below. Determine the expected value for each alternative using the given probabilities.

Acquire Stable economy (0.65) Slowing economy (0.35)

4,000 sq. ft, new trucks $105,000 -$65,450

4,000 sq. ft, keep truck $84,200 -$25,300

2,000 sq. ft, new trucks $74,350 -$38,900

2,000 sq. ft, keep truck $56,750 -$15,250

(Points : 6)

Question 11. 11. Construct a Gantt chart for the following set of activities. Indicate the total project completion time and the slack for

each activity. Submit a plain text version of your Gantt chart by using dashes to represent activity lengths (e.g., —- for 4 weeks).

Activity Predecessor Time (weeks)

1 – 4

2 – 2

3 – 6

4 1 6

5 3 8

6 4,5 4

7 6 3

8 2 10

(Points : 4)

Question 12. 12. Using the CPM/PERT network below, with times measured in days, find the critical path and the slack times for each step.

What is the project completion time? For each node, the step number is written on top and the time written on the bottom.

(Points : 5)

Question 13. 13. Using the activity table below, construct a CPM/PERT network noting the activity numbers and durations. Identify the

critical path through the network, determine the project completion time, and determine the earliest and latest start dates for each node.

Create your network in Microsoft Word and submit it to your instructor.

Activity Predecessor Time (days)

1 – 2

2 – 8

3 1 3

4 1,2 6

5 3 3

6 3 5

7 4,5,6 10

(Points : 6)

Question 14. 14. Use the activity table below to determine the expected activity lengths and variances for each of the activities, using

the beta distribution.

Activity Time estimates: a, m, b (days)

1 3, 10, 20

2 3 ,5, 8

3 2, 6, 14

4 12, 20, 32

(Points : 5)

Question 15. 15. Use the activity table below. Find the project completion time. What is the combined cost of tasks on the critical path

only?

Activity Predecessor Time: (weeks) Cost: ($)

1 – 6 6,400

2 – 2 2,500

3 1 4 5,500

4 2 5 6,400

5 3, 4 6 6,600

(Points : 4)

Question 16. 16. Solve the linear programming problem.

Minimize Z = 42x + 10y

subject to

2x + 2y ≥ 80

x + 6y ≥ 200

x, y ≥ 0 (Points : 4)

Question 17. 17. Solve the linear programming problem by graphing. Graph the feasible region, list the extreme points and identify the

maximum value of Z. You do not have to submit your graph, but please list the equations of the lines that form the feasible region.

Minimize Z = 4x + 6y

subject to

2x + 4y ≥ 20

3x + 2y ≤ 24

x, y ≥ 0 (Points : 5)

Question 18. 18. Turbo Coolers Inc. builds cooling systems for industrial plants. A Type A cooler takes 80 W of power and can cool 18

liters of fluid per minute under the given conditions. A Type B cooler takes 100 W of power and can cool 60 liters of fluid per minute. A

Type A cooler costs $3,500 and a Type B cooler costs $12,000. The factory has up to 1,000 W of power it can supply for cooling, and must

cool 300 liters of fluid per minute. How many of each type of cooler should Turbo Coolers Inc. install in the factory to minimize cost?

Formulate a linear programming model for this situation. Solve this model using graphical analysis. Display your graph and the solution

parameters. Create your graph using Microsoft Word or Excel and submit it to your instructor.Create your graph using Microsoft Word or

Excel and submit it to your instructor. (Points : 6)

Question 19. 19. The New Kilkenny Highway Commission is installing a camera-based highway monitoring system to track the license plate

numbers of cars entering and leaving the highway. They are examining two different camera systems. System A can track three cars per

second, takes up 1 foot of space on the overhead beams, and costs $4,000. System B can track 13 cars per second, takes up 5 feet of space

on the overhead beams, and costs $10,000. The highway commission cannot spend more than $80,000 for the system, and has 25 feet of

overhead beam space available. Formulate a linear programming model to maximize the number of cars the system can track. List the extreme

points and determine the solution graphically. You do not need to submit your graph. (Points : 6)

Question 20. 20. Three Ships Winery produces two different wine blends. A batch of the Dark Night blend uses 4 tons of malbec grapes and 2

tons of merlot grapes. A batch of the Morning Star blend uses 2 tons of malbec grapes and 4 tons of merlot grapes. The winery has a total

of 18 tons of malbec grapes, and 18 tons of merlot grapes.The profit for a batch of Dark Night is $14,500 and the profit for a batch of

Morning Star is slightly less at $12,250. How many batches of each type of wine should the winery produce this year to maximize its

profit, assuming half batches are allowed? Formulate a linear programming model and solve it graphically. Display your graph and calculate

the maximum profit. Create your graph using Microsoft Word or Excel and submit it to your instructor. (Points : 7)

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