Question

100 points

Find the maximum value of the objective function and the values of x and y for which it occurs.
f=5x+2y
x+2y
`\leq`=6 x
`\geq`=0 and y
`\geq`=0
2x+y
`\leq`=6

Answer 1

Maximum value of the objective function is 15

This occurs at x = 3, y = 0

Explanation:

Attached is a plot of the two inequalities. The feasible region is the dark shaded area bounded by the points O, A, B and C

The maximum value of the objective function will occur at one of the corner points

The four corner points are

O (0,0)

A(0,3)

B(2,2)

C(3,0)

Plug in each of these values into the objective function, see which of the corner points will yield the maximum value and those will be the optimal values of x and y

Corner point (x, y) O.F Value (5x + 2y)

(0, 3) 5(0) + 2(3) = 6

(2, 2) 5(2) + 2(2) = 14

(3, 0) 5(3) + 2(0) = 15 (Maximum value)