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Answer:

The maximum value of the function = 11, at x = 3 and y = 5

The minimum value of the function = -21, at x = 3 and y = -3

Step-by-step explanation:

Given;

F = 4y - 3x

The function is subject to  y ≤ 2x - 1,

                                            y ≥ -2x + 3,

                                               x ≤ 3

           y ≤ 2x - 1  

      -  ( y ≥ -2x + 3)

        -------------------

          0 ≤ 4x - 4

           4 ≤ 4x

            1 ≤ x

thus,   1 ≤  x ≤ 3

When x = 3

y ≤ 2x - 1     ⇒     y ≤ 2(3) - 1,        ⇒ y ≤ 5

y ≥ -2x + 3,  ⇒    y ≥ -2(3) + 3,      ⇒ y ≥ - 3

thus, -3 ≤  y  ≤ 5

When x = 1

y ≤ 2x - 1     ⇒     y ≤ 2(1) - 1,        ⇒ y ≤ 1

y ≥ -2x + 3,  ⇒    y ≥ -2(1) + 3,      ⇒ y ≥ 1

when x = 1 and y = 1

F = 4(1) - 3(1)

F = 1

when y = -3, and x = 3

F = 4(-3) - 3(3)

F = -12 - 9

F = - 21

When y = 5 and x = 3

F = 4(5) - 3(3)

F = 20 - 9

F = 11

Therefore, the maximum value of the function = 11, at x = 3 and y = 5

The minimum value of the function = -21, at x = 3 and y = -3

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