# Decision Theory - Expected Values

The concessions manager at our local college baseball game must decide whether to have the vendors sell sun visors or umbrellas. There is a 30% chance of rain, a 15% chance of overcast skies, and a 55% chance of sunshine, according to the weather forecast where the game is to be held. The manager estimates the following profits will result from each decision given each set of weather conditions.

Weather Conditions

Decision Rain .30 Overcast .15 Sunshine .55

Sun visors $-500 $-200 $1,500

Umbrellas $2,000 0 -900

a. I need to compute the expected value for each decision and select the best one using the Optimistic and Pessimistic approach.

b. I also need to develop the opportunity loss table and compute the expected opportunity loss for each decision and determine the "minmax regret".

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#### Solution Preview

expected profit when vendor sells sun visors = .30*-500 + .15*-200+.55*1500 = 645

expected profit when vendor sells umbrellas =.30* 2000+ .15* 0 +.55*-900 = 105

Since the expected profit of sun visors is more than umbrellas the vendors should sell Sun visors.

opportunity loss table:

Take maximum in each column and subtract the maximum value and the ...