Question

Maximize the objective function p = 3x + 5y for the given constraints. Find the maximum value of p subject to the following constraints:

1) x ≥ 0, y ≥ 0
2) x * y ≤ 5
3) 3x + 6y ≤ 21

Answer 1

To maximize the objective function p = 3x + 5y, graph the feasible region and find the corner point that gives the maximum value of p.

Step-by-step explanation:

To maximize the objective function p = 3x + 5y, subject to the given constraints, we first need to graph the feasible region and then find the corner point that gives the maximum value of p.

1. Graph the constraint x * y ≤ 5 on the xy-plane. The feasible region is the shaded region where the constraint is satisfied.
2. Graph the constraint 3x + 6y ≤ 21. The feasible region is the shaded region where both constraints are satisfied.
3. Find the corner points of the feasible region.
4. Substitute each corner point into the objective function p = 3x + 5y.
5. Compare the values of p at each corner point and identify the maximum value of p.

By following these steps, you will be able to find the maximum value of p subject to the given constraints.