请帮忙求解
MacBurger has just opened a fast-food restaurant in Bloomington.Currently,i0 customers frequent MacBurger(we call these loyal customers),and N-i0 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)