Question

The Video Game Supply Company (VGS) is deciding whether to set next year's production at 2000, 2500, or 3000 games. Demand could be low, medium, or high. Using historical data, VGS estimates the probabilities as: 0.4 for low demand, 0.3 for medium demand, and 0.3 for high demand. The following profit payoff table (in $100s) has been developed. Production Target Demand Low Medium High 2000 games 1000 1200 1400 2500 games 800 1500 1300 3000 games 600 1700 1400

[1] What is the maximax decision alternative? [1] What is the maximin decision alternative? [2] Determine the expected value of each alternative and indicate what should be the production target for next year based on expected value. [1] Determine the expected value with perfect information about the states of nature. [1] Determine the expected value of perfect information.

Answer 1

Solution:

a)

For EMV :

Quantity	Probability	Production target
Demanded		2000	2500	3000
Low	0.4	1000	800	600
Medium	0.3	1200	1500	1700
High	0.3	1400	1300	1400
Expected Monetary Value( EMV )		1180	1160	1170

The EMV corresponding to production target of 2000 units is the maximum

So, production target should be 2000 units for a maximum EMV of 1180( in $100)

b)

Expected value with perfect information about states of nature is also known as Expected payoff or profit with perfect information i. EPPI

Expected Profit Table with perfect Information ($100)

States of Nature ( Quantity Demanded )	Conditional Profit under Certainty	Probability	Expected profit with perfect information
Low	1000	0.4	400
Medium	1700	0.3	510
High	1400	0.3	420

Expected Profit with perfect Information is ( EPPI ) = 1,330

c)

Expected value of perfect information ( EVPI) = EPPI - Maximum EMV

= 1330 - 1180

= 150

Expected value of perfect information ( EVPI) = 150 ($100)