11 Georgia Stein is the new owner of the New York Yankees. Each season, Georgia must decide how much money to spend on the free agent draft. During each season, Georgia can spend any amount of money on free agents up to the team’s capital position at the beginning of the season.

If the Yankees finish in ith place during the season, their capital position increases by R(i) dollars less the amount of money spent in the free agent draft. If the Yankees finished in ith place last season and spend d dollars on free agents during the off-season, the probability that the Yankees will finish in place j during the next season is pij(d)( j  1, 2,

. . . , 7). Last season, the Yankees finished in first place, and at the end of the season, they had a capital position of D dollars. Formulate a dynamic programming recursion that will enable the Yankees to maximize their expected cash position at the end of T seasons.