Given the system of constraints, name all vertices of the feasible region. Then find the maximum value of the given objective function.
constraints:
x≥0
y≥0
y≤1/3 x+3
5≥x+y
objective function:
c = 6x-4y
Vertices of the feasible region are: (0,0), (4,0), (5,0), (0,4), and (0,5/3).
To find the maximum value of the objective function, substitute the coordinates of each vertex into the objective function:
c(0,0) = 6(0) - 4(0) = 0
c(4,0) = 6(4) - 4(0) = 24
c(5,0) = 6(5) - 4(0) = 30
c(0,4) = 6(0) - 4(4) = -16
c(0,5/3) = 6(0) - 4(5/3) = -20/3
Therefore, the maximum value of the objective function is 30 at the vertex (5,0).