In Example 2, change the last constraint to 3y − x ≤ 4. Then graph the feasible points and find the maximum and minimum values of F.

Data from Example 2

Find the maximum and minimum values of the objective function F = 3x + y, subject to the constraints

The constraints are graphed as shown in Fig. 17.45. We then locate the vertices, and evaluate F at these vertices as follows.

Therefore, we see that the maximum value of F is 24, and the minimum value of F is 6. If we check the value of F at any other feasible point, we will find a value between 6 and 24.

x 2, y 0 x + y 8 2y x 1 =