8 MacBurger has just opened a fast-food restaurant in Bloomington. Currently, i0 customers frequent MacBurger

(we call these loyal customers), and Ni0 customers frequent other fast-food establishments (we call these nonloyal customers). At the beginning of each month, MacBurger must decide how much money to spend on advertising. At the end of a month in which MacBurger spends d dollars on advertising, a fraction p

(d) of the loyal customers become nonloyal customers, and a fraction q

(d) of the nonloyal customers become loyal customers. During the next 12 months, MacBurger wants to spend D dollars on advertising.
Develop a dynamic programming recursion that will enable MacBurger to maximize the number of loyal customers the company will have at the end of month 12. (Ignore the possibility of a fractional number of loyal customers.)