Question

Find the optimal solution for the following problem. Maximize C = 4x + 12y + 3z subject to 15x + 5y + 12z ≤ 75 6x + 2y + 8z ≤ 150 and x ≥ 0, y ≥ 0.

Answer 1

Given that,

Maximize C = 4x + 12y + 3z subject to 15x + 5y + 12z ≤ 75 6x + 2y + 8z ≤ 150 and x ≥ 0, y ≥ 0 and z ≥ 0,

Here, x = X1, y = X2, z = X3, C = Z,

Calculation:

Pivot row (Row 1): 75 / 5 = 15 15 / 5 = 3 5 / 5 = 1 12 / 5 = 12 / 5 1 / 5 = 1 / 5 0 / 5 = 0 Row 2: 150 - (2 * 15) = 120 6 - (2 * 3) = 0 2 - (2 * 1) = 0 8 - (2 * 12 / 5) = 16 / 5 0 - (2 * 1 / 5) = -2 / 5 1 - (2 * 0) = 1 Row Z: 0 - (-12 * 15) = 180 -4 - (-12 * 3) = 32 -12 - (-12 * 1) = 0 -3 - (-12 * 12 / 5) = 129 / 5 0 - (-12 * 1 / 5) = 12 / 5 0 - (-12 * 0) = 0

or, as per question, x= 0, y=15, z=0, Maximize C = 180