Question

Consider the following linear program with two decision variables, A and B:

max A + B
s.t. A + 2B ≤ 60
3A + 2B ≤ 120
A, B ≥ 0
Use the graphical solution method to determine the optimal solution and the associated objective function value.

Answer 1

To find the optimal solution and associated objective function value for the given linear program, we can use the graphical solution method.

Step-by-step explanation:

To solve this linear program using the graphical solution method, we need to find the feasible region and then locate the point that maximizes the objective function.

Step 1:

Plot the boundary lines of the constraints:

A + 2B = 60

3A + 2B = 120

Step 2:

Identify the feasible region by shading the area that satisfies all the constraints.

Step 3:

Plot the objective function A + B as a line with slope -1 (because the objective function is maximized when A and B are minimized).

Step 4:

The optimal solution is the point of intersection between the objective function line and the feasible region boundary. The associated objective function value is the sum of the A and B coordinates of the optimal solution.