The LP below has optimal solution x* = (5, 0, 0, 0, 2) with z* = 60 and basic solution of x_B = (x1, x3, x5).

Maximize z = 12x₁ + 6x₂ + 2x₃

subject to 2x₁ + 4x₂ x₃ + x₄ = 10

x₁ + 3x₃ = 5

x₁ + 2x₂ x₅ = 3

x_j 0, j = 1, , 5

Compute simple ranges over which the basis does not change for each of objective function coefficient and right-hand-side constant.

Hint: You need to perform sensitivity analysis for both objective function coefficients and right-hand-sides.

The LP below has optimal solution x* = (5, 0, 0, 0, 2) with z* = 60 and basic solution of xB = (X1, X3, X5). Maximize subject to z=12x1 + 6x2 + 2x3 2x + 4x2 x3 + x4 = 10 X1 + 3x3 = 5 x + 2x2 - X5 = 3 Xj0, j= 1, ..., 5 Compute simple ranges over which the basis does not change for each of objective function coefficient and right-hand-side constant. Hint: You need to perform sensitivity analysis for both objective function coefficients and right-hand-sides