What is the minimum value for z 3x 1 2y over the feasibility region defined by the constraints shown below? x>0yxy>-1/2x 6

The minimum value for z = 3 x - 1/2 y over the feasibility region is where x has the minimum value and y has the maximum value.

x ≥ 0, y ≤ 8, y ≥ x and y ≥ - 1/2 x + 6

Those values are: x = 0 and y = 8

z min = 3 · 0 - 1/2 · 8 = 0 - 4 = - 4

Answer: A) - 4