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XII. (22 points) Consider the following items in the Knapsack Problem: Item weight value Knapsack capacity W = 11. ?? ? ? $8 $1 $15 ? In the Fractional Knapsack Problem, what is the maximum value that can be put in the knapsack? (a) $15 (b) $23 (c) $25 (d) $19 o Using the same items as in part (a), the Dynamic Programming approach outlined in the book and discussed in class produces a (n + 1) x (W+ 1) table containing the maximum values P[i][w] for a knapsack of capacity w, considering the first i items. W? d i 4 5 6 7 8 6 10 4 1 0 0 0 3 3 3 3 3 3 3 3 3 2 0 0 0 3 8 8 8 11 11 11 11 11 3 0 0 1 3 8 8 9 11 11 12 12 12 4 0 0 1 3 8 15 15 16 18 23 ? ? Compute the missing values in this table using the formula outlined in the textbook and in class P[4][10] = P[4][11]= Starting from the value of P[4][11] (the maximum profit for the 0-1 Knapsack in this case) which items are placed in the knapsack to achieve this maximum value