A manufacturer makes custom tee shirts for rock groups. The manufacturer makes a

Question

A manufacturer makes custom tee shirts for rock groups. The manufacturer makes a profit of $15 per tee shirt. The fixed costs of building a large facility are $100,000 and the fixed costs of building a small facility are $60,000. The production levels for the large facility are 5,000, 10,000,20,000 and 30,000; the small facility can only produce up to 20,000 level. The probabilities associate d with the different levels of production are .15, .25, .4, & .2 respectively.

a. Compute the payoffs based on this data.

b. Construct a Payoff Table.

c. Construct an Opportunity Loss Table.

d. Construct an Expected Monetary Value Table.

e. Construct an Expected Opportunity Loss Table (You must construct the chart)

f. What is the value of Perfect Information? (You must show calculations)

Explanation / Answer

Solution

Part (a)

Let xi be the ith production level. Then, total profit = 15xi since manufacturer makes a profit of $15 per tee shirt.

So, pay-off = 15xi - fixed costs of building the facility .

Thus,

pay-off is 15xi - 100,000 for large facility and 15xi - 60,000 for small facility ANSWER

Part (b)

Pay-off Table ($)

Facility

Production Level

5000

10000

20000

30000

Large

- 25000

50000

200000

350000

Small

15000

90000

240000

Not applicable

DONE

Part (c)

Opportunity Loss for a strategy (decision option: large/small facility) under a given SON, i.e., State of Nature (production level in the present case) = best pay-off under the given SON – pay-off for the strategy under that SON.

Pay-off and Opportunity Loss Table ($)

[main entry is pay-off and figures within bracket are OL]

Facility

Production Level

5000

10000

20000

30000

Large

- 25000 (40000)

50000 (40000)

200000 (40000)

350000 (0)

Small

15000 (0)

90000 (0)

240000 (0)

Not applicable

Part (d)

Expected Monetary Value (EMV) = sum of (pay-off x probability of SON), summed over all possible SON.

EMV TABLE FOR LARGE FACILITY

Production Level

5000

10000

20000

30000

Probability (p)

0.15

0.25

0.40

0.20

Pay-off (P)

- 25000

50000

200000

350000

P x p

- 3750

12500

80000

70000

EMV = sum of (P x p) = $158750 ANSWER 1

EMV TABLE FOR SMALL FACILITY

[Since small facility cannot reach the 30000 level, but total probability has to be 1, probability 0.2 of 30000 is proportionately distributed among the other levels by multiplying by a factor of 1/0.8 = 1.125 ]

Production Level

5000

10000

20000

Probability (p)

0.1875

0.3125

0.50

Pay-off (P)

15000

90000

240000

P x p

2812.5

28152

120000

EMV = sum of (P x p) = $150964.50 ANSWER 2

Facility

Production Level

5000

10000

20000

30000

Large

- 25000

50000

200000

350000

Small

15000

90000

240000

Not applicable

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