Question

Find the minimum and maximum values of z = 9x + 4y, if possible, for the following set of constraints.

x + y ≤ 9
- x+ y ≤ 3
2x - y ≤12

Answer 1

To find the minimum and maximum values of z for the given constraints, graph the constraints to determine the feasible region, calculate z at each corner point, and identify the largest and smallest values found.

Step-by-step explanation:

To find the minimum and maximum values of z = 9x + 4y given the constraints:

• x + y ≤ 9
• -x + y ≤ 3
• 2x - y ≤ 12

We use the method of linear programming.

A step by step explanation:

1. Graph the constraints to identify the feasible region.
2. Find the corner points of the feasible region.
3. Evaluate the objective function z at each corner point.
4. The largest and smallest values obtained are the maximum and minimum values of z.

Without graphing, we cannot provide the exact values, yet the process will reveal the minimum and maximum as long as the feasible region is bounded.