Farmer Jones now possesses $5,000 in cash and 1,000 bushels of wheat. During month t, the price of wheat is pt. During each month, he must decide how many bushels of wheat to buy (or sell). There are three restrictions on each month’s wheat transactions: (1) During any month, the amount of money spent on wheat cannot exceed the cash on hand at the beginning of the month; (2) during any month, he cannot sell more wheat than he has at the beginning of the month; and (3) because of limited warehouse capacity, the ending inventory of wheat for each month cannot exceed 1,000 bushels.

Show how dynamic programming can be used to maximize the amount of cash that farmer Jones has on hand at the end of six months.