Final answer:
To maximize the objective function p = 80x + 55y, we graph the constraints to find the feasible region and then evaluate the objective function at the corners of this region, selecting the vertex with the highest value for p.
Step-by-step explanation:
The student is asking how to maximize the objective function p = 80x + 55y, given a set of linear constraints. To maximize this objective function, we need to graph the constraints and find the feasible region. Then, we will evaluate the objective function at the vertices (corner points) of the feasible region to find the maximum value.
- Firstly, graph the inequalities x ≥ 0, y ≥ 0, 4x + 3y ≤ 44, and 2x + 5y ≤ 36.
- Identify the feasible region that satisfies all constraints.
- Calculate the objective function at each vertex of the feasible region.
- Select the vertex that gives the highest value for p.
This is the point where the objective function is maximized.