Buying and Selling a Commodity. A small firm buys and sells wheat. They own a warehouse with a capacity of 10,000 bushels, and as of late August, there will be 2,000 bushels in the warehouse. Wheat is delivered to the warehouse during the first week of the month, and it is sold and shipped around the middle of the month. All transactions are on a cash basis because the season is short, and the firm expects to have $20,000 in its accounts at the end of August. This amount is available for making September purchases. The latest predictions of market prices are shown in the following table:

a. What buy-and-sell schedule will produce the maximum profit for the firm?
b. What is the optimal profit in part (a)?
c. How does the optimal plan change as a function of the firm’s account balance? (Consider amounts both above and below the current $20,000.)

 

Sep 15 Oct 15 Nov 15 Buy $5.45 $5.75 $6.00 Sell $6.05 $6.25 $6.30