Question

By graphing the system of constraints and using the values of x and y that maximize the objective function, find the maximum value for P in the linear programming problem where: 6 ≤ 3x and y ≥ 1. Maximize for P = 4x + 3y

A) P = 51
B) P = 27
C) P = 38
D) P = 35

Answer 1

To find the maximum value for P in the given linear programming problem, graph the system of constraints and use the values of x and y that maximize the objective function. The maximum value for P is 11.

Step-by-step explanation:

To find the maximum value for P in the given linear programming problem, we need to graph the system of constraints and use the values of x and y that maximize the objective function. The system of constraints is:

6 ≤ 3x

y ≥ 1

The objective function is P = 4x + 3y. To graph the system of constraints, we can start by plotting the lines 6 = 3x and y = 1 on a coordinate plane. The feasible region is the shaded area that satisfies both constraints. Next, we substitute the coordinates of the vertices of the feasible region into the objective function to find the maximum value for P. The vertex that maximizes P is (2, 1) with a value of P = 4(2) + 3(1) = 11.

Therefore, the maximum value for P is 11.