Question

what is the minimum value for z=4x - 1/3y over the feasibility region defined by the constraints shown above

Answer 1

The vertex of the feasibility region are (0, 0), (0, 5), (4, 0) and (14, 5)

For (0, 0): z = 4(0) - 1/3(0) = 0
For (0, 5): z = 4(0) - 1/3(5) = -5/3
For (4, 0): z = 4(4) - 1/3(0) = 16
For (14, 5): z = 4(14) - 1/3(5) = 56 - 5/3 = 163/3

Therefore, the minimum value is z = -5/3 at point (0, 5).