Let n = 4,(p1,p2,p3,p4) = (100,10,15,27) and (d1,d2,d3,d4)=(2,1,2,1). Find the optimal solution among given feasible solutions:a.(1,4)b.(3,4)c.(1,2)d.(2,3)

The problem seems to be a variant of the Knapsack problem, where we have n items, each with a profit (p) and a weight (d). We want to maximize the total profit while ensuring that the total weight does not exceed a certain limit. However, the limit is not given in the problem.

Assuming that the pairs in the feasible solutions represent the indices of the items to be included in the knapsack, we can calculate the total profit and weight for each feasible solution:

a. (1,4): Total profit = p1 + p4 = 100 + 27 = 127, Total weight = d1 + d4 = 2 + 1 = 3 b. (3,4): Total profit = p3 + p4 = 15 + 27 = 42, Total weight = d3 + d4 = 2 + 1 = 3 c. (1,2): Total profit = p1 + p2 = 100 + 10 = 110, Total weight = d1 + d2 = 2 + 1 = 3 d. (2,3): Total profit = p2 + p3 = 10 + 15 = 25, Total weight = d2 + d3 = 1 +