Expected profit, mean-variance, maximin, maximax

A firm making production plans believes there is a 30% probability the price will be \$10, a 50% probability the price will be \$15%, and a 20% probability the price will be \$20. The manager must decide whether to produce 6000 units of output (A), 8000 units (B) or 10000 units (C). The following table shows 9 possible outcomes depending on the output chosen and the actual price.

Profit (loss)when price is
\$10 \$15 \$20

6,000 (A) (\$200) \$400 \$1,000
Production 8,000 (B) (\$400) \$600 \$1,600
10,000 (C) (\$1,000) \$800 \$3,000

11. What is the expected profit if 6000 units are produced?

a. \$171
b. \$840
c. \$640
d. \$340
e. \$260

12. What is the expected profit if 10,000 units are produced?
a. \$500
b. \$700
c. \$625
d. \$1000
e. \$1754

13. If the mean-variance rule is used, how much should the firm produce?
a. 6,000
b. 8,000
c. 10,000
d. can’t use this rule to make the decision

14. What is the variance if 6,000 units are produced?
a. 490,000
b. 176,400
c. 100,000
d. 68,200
e. 76,460

15. For the above payoff matrix, suppose the manager has no idea about the probability of any of the three prices occuring. If the maximax rule is used how much will the firm produce?
a. 6,000
b. 8,000
c. 10,000
d. can’t use this rule to make the decision.

16. For the above payoff matrix, suppose the manager has no idea about the probability of any of the three prices occuring. If the maximin rule is used how much will the firm produce?
a. 6,000
b. 8,000
c. 10,000
d. can’t use this rule to make the decision

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