4. Solve the following 0/1 knapsack problem using dynamic programming where the knapsack capacity is 7. You need to find the maximum profit and the list of items to be taken for the maximum profit. [Marks: 5] Item Weight Profit 1 1 12 2 2 10 3 3 20 4 1 15 5 2 45
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The knapsack problem involves selecting a set of items to maximize the total profit while not exceeding the weight capacity of the knapsack. Next, we need to understand the given input. We have a list of items, each with a weight and a profit value. We also have Show more…
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Akash M.
The knapsack problem is to determine how many units of each item to place in the knapsack to minimize the number of items in the knapsack, maximize the number of items in the knapsack, maximize total value, and minimize total value.
Rashmi S.
Solve the following knapsack problem using the branch-and-bound algorithm. Maximize 8x1 + 5x2 + 9x3 + 10x4 + 5x5 Subject to 2x1 + 2x2 + 4x3 + 5x4 + 3x5 ≤ 12, x1, ..., x5 ∈ {0, 1} Note that the variables appear in decreasing order of cj/wj (value over weight). As a consequence: - The optimal LP solution is to make each variable in turn from left to right as large as possible. You will generally set some to 1 and then have one variable that has to take a fractional value. At each step, you'll branch on the fractional variable. - You can get a heuristic solution (quick, but not necessarily optimal) using a greedy algorithm: set variables to 1 in left-to-right order, skipping ones that don't fit. In this case, the greedy solution is x = (1, 1, 1, 0, 1) with an objective value of 27. You can use that solution as your starting incumbent.
Madhur L.
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