Given the system of constraints, name all the vertices of the feasible region. Then find the maximum value of the given objective function.

x>=0

y>=0

y=<1/3x+3

5>=y+x

Objective Function: C=6x-4y

The vertices of the feasible region are: (0, 0), (0, 3), (1.5, 3.5), (5, 0)

For (0, 0) : C = 6 (0) - 4 (0) = 0

For (0, 3) : C = 6 (0) - 4 (3) = - 12

For (1.5, 3.5) : C = 6 (1.5) - 4 (3.5) = 9 - 14 = - 5

For (5, 0) : C = 6 (5) - 4 (0) = 30

Therefore, the maximum value of the ob jective function is 30.