Consider the following linear program.

Max 3A + 2B

s.t.

1A + 1B 10

3A + 1B 22

1A + 2B 18

A, B 0

(a) Use the graphical solution procedure to find the optimal solution. (Graph the constraint lines, the feasible region, the objective function line, and the optimal solution. Graph all lines as solid lines.)

What is the value of the objective function at the optimal solution?

_____ at (A,B)= (_____)

(b) Assume that the objective function coefficient for A changes from 3 to 5. Use the graphical solution procedure to find the new optimal solution. (Graph the constraint lines, the feasible region, the objective function line, and the optimal solution. Graph all lines as solid lines.)

Does the optimal solution change?

The extreme point (_______) (remains or becomes) optimal. The value of the objective function becomes ________.

(c) Assume that the objective function coefficient for A remains 3, but the objective function coefficient for B changes from 2 to 4. Use the graphical solution procedure to find the new optimal solution. (Graph the constraint lines, the feasible region, the objective function line, and the optimal solution. Graph all lines as solid lines.)

Does the optimal solution change?

The extreme point (______) (remain or become) optimal. The value of the objective function becomes ________.