10. (20 pts) Consider the 0-1-2-3-4 Knapsack Problem obtained by replacing the 0/1 constraint of the 0/1 knapsack problem by xi=0 or 1 or 2 or 3 or 4 instead (i.e., we assume four copies of the ith object are available, for all i ). Description of the 0-1-2-3-4 Knapsack Problem is given as follows. 0-1-2-3-4 Knapsack Problem: Instance: n objects, p1,p2,,pn profits, knapsack of capacity M,w1,w2,,wn weights Question: To find x1,x2,,xn s.t. pixi is maximized subject to wixiM where For the dynamic programming functional equation to solve the 0-1-2-3-4 Knapsack Problem, we define fi(X)= max profit generated after considering the first i objects (or values of x1,x2,,xi ) subject to capacity X. (a) (4pts) f0(X)=,0XM (b) (10 pts) We assume that fi(X)=,0i<>