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.

Solve the 0/1 Knapsack problem given that: The Knapsack can only carry a maximum of 8 Kg. The items are 2 Kg with a value of Ksh 100, 3 Kg with a value of Ksh 120, 5 Kg with a a value of Ksh 140, 1 Kg with a value of Ksh 60, and 6 Kg with a value of Ksh 150.

You have to solve it Using Python Programming language.

A person is cutting a long board of wood into different length of pieces . Each cutting has fixed width 2 cm lengths. Given that each cutting with different length has a different price, Now, we are required to help this person to find the optimal cuts in order to increase his income. Consider following example showing different cut’s lengths and their equivalent prices. Input: board length = 4 Length [ ] = [1, 2, 3, 4, 5, 6, 7, 8] Price [ ] = [2, 6, 8, 10, 14, 17, 19, 20] Output: Best cut is two pieces of length 2 each to gain revenue of 6 + 6 = 12 [Explanation: the possible cuts and profit of each is as follows: As noted the best cut is two pieces of length 2 each to gain revenue of 6 + 6 = 12

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.