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).
