Question: Problem 3: Integer Programming and Dynamic Programming (25 points) You are given a knapsack with maximum weight 5. Now there are three types of items

Problem 3: Integer Programming and Dynamic

Problem 3: Integer Programming and Dynamic Programming (25 points) You are given a knapsack with maximum weight 5. Now there are three types of items in which you can put them into the knapsack (to maximize total value). Item Type 1: Value vi = 7, Weight wi = 1 Item Type 2: Value v2 = 20, Weight W2 = 3 Item Type 3: Value V3 = 15, Weight W3 = 2 Note that you are allowed to put more than one of each item type into the knapsack. (a) Formulate this problem as an integer program. (5 points) (b) Numerically solve this problem via dynamic programming (starting from item 3, 2, 1). (20 points)

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