Consider that there are four items that can fit inside a 13-pound-capacity backpack. The respective weights of the items are 5.7, 4, and 3 pounds. Their respective utilities are 8, 11, 6, and 4 utils. Determine the optimal solution that maximizes the overall usefulness of the backpack.

Any linear program L, given in standard form, either1. has an optimal solution with a finite objective value,2. is infeasible, or3. is unbounded.If L is infeasible, SIMPLEX returns “infeasible.” If L is unbounded, SIMPLEXreturns “unbounded.” Otherwise, SIMPLEX returns an optimal solution with a finiteobjective value.

Any linear program L, given in standard form, either1. has an optimal solution with a finite objective value,2. is infeasible, or3. is unbounded.If L is infeasible, SIMPLEX returns “infeasible.” If L is unbounded, SIMPLEXreturns “unbounded.” Otherwise, SIMPLEX returns an optimal solution with a finiteobjective value.