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.

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