Consider the following input and fill the table corresponding to the recursion you found in #1: n = 6, w1 = 1, w2 = 3, w3 = 2, w4 = 5, w5 = 4, w6 = 7, v1 = 2, v2 = 3, v3 = 5, v4 = 7, v5 = 11, v6 = 13 and W = 10. Moreover, give all optimal solutions.

#1)

You are given n objects which cannot be broken into smaller pieces. Moreover, you have exactly one copy of each object. Each object i (where 1-i-n) has weight wi 0 and value vi 0. You have a knapsack that can carry a total weight not exceeding W. Your goal is to fill the knapsack in a way that maximizes the total value of the included objects, while respecting the capacity constraint. For each object i (where 1