A retailer buys bushels of mushrooms for $2 each and sells them for $5 each. The quality of the mushrooms begins to decline after the first day they are offered for sale; therefore, to sell the mushrooms for $5/bushel, he must sell them on the first day. Bushels not sold on the first day can be sold to a wholesaler who buys day-old mushrooms at the following rates.

A 90-day observation of past demand yields the following information:

a. Set up a payoff table that could be used by the retailer to decide how many bushels to buy.
b. Find the optimal number of bushels the retailer should buy to maximize profit.

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Amount purchased (bushels) Price per bushel 4 or more $1.25 3 2 3 1 $2.00 $1.75 $1.50 Daily demand (bushels) 10 9. 12 11 18 13 Number of days 27 36