[Knapsack Covers] Consider the binary knapsack problem max x + 2x2 + x3 + 7x4 s.t. 100xi + 70x2 +50x3 + 60x4 150 Since not all variables in the cover S can be in the knapsack simultaneously, we can enforce the cover inequality Xi SS1-1 IES X1 + X2 + X3 + X4 4-1-3 Note, however, that there are other covers that use fewer variables. A minimal cover is a subset of variables such that no other subset of those variables is also a cover. For example, consider the cover S' = {1,2). This is a cover since 100 + 70 > 150. Since S' is a subset of S, the cover S is not a minimal cover. In fact, S' is a minimal cover since there are no smaller subsets of the set S' that also produce a cover. In this case, we call the corresponding inequality animal cover inequality. That is, the inequality is a minimal cover inequality for this problem. The minimal cover inequalities are the "strongest" of all cover inequalities. [To do:] Find the two other minimal covers (one of size 2 and one of size 3) and write their corresponding minimal cover inequalities. [Knapsack Covers] Consider the binary knapsack problem max x + 2x2 + x3 + 7x4 s.t. 100xi + 70x2 +50x3 + 60x4 150 Since not all variables in the cover S can be in the knapsack simultaneously, we can enforce the cover inequality Xi SS1-1 IES X1 + X2 + X3 + X4 4-1-3 Note, however, that there are other covers that use fewer variables. A minimal cover is a subset of variables such that no other subset of those variables is also a cover. For example, consider the cover S' = {1,2). This is a cover since 100 + 70 > 150. Since S' is a subset of S, the cover S is not a minimal cover. In fact, S' is a minimal cover since there are no smaller subsets of the set S' that also produce a cover. In this case, we call the corresponding inequality animal cover inequality. That is, the inequality is a minimal cover inequality for this problem. The minimal cover inequalities are the "strongest" of all cover inequalities. [To do:] Find the two other minimal covers (one of size 2 and one of size 3) and write their corresponding minimal cover inequalities