Solve using fractional knapsack:

M=20, n=4

P= (3, 10, 15, 5)

W= (5, 13, 12, 8).

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The fractional knapsack problem involves selecting items to fill a knapsack of limited capacity (M=20 in this case) in such a way as to maximize the total value.

Here’s how to solve it:

So the optimal solution is to choose items 3, 2 and a fraction of item 1, with a total value of 22.