12. Solve the following problem by DP:

Maximize z = (YI + 2)2 + Y2Y3 + (Y4 - 5)2 subject to YI + Y2 + )'3 + Y4 :s; 5

)'i ;:::: °and integer, i = 1,2,3,4 13. Solve the following problem by DP:

Minimize z = max{f(yd,f(}2),· .. ,f(YII)}

subject to Yl + }2 + ... + Yn = c Yi 2 0, i = 1,2, ... , n Provide the solution for the special case of n = 3, c = 10, and f(yd = )'1 + 5,

!(}2) = 5)'2 + 3, and f(.Y3) = Y.3 - 2.