Consider the following linear program. Max 3A + 2B 5.t. 1A + 1B S 10 3A + 1B $ 22 1A + 2B S 16 AB A, B 20 (a) Use the graphical solution procedure to find the optimal solution. What is the value of the objective function at the optimal solution? x at (A,B) = X (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. Does the optimal solution change? The extreme point remains 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 changes from 2 to 4. Use the graphical solution procedure to find the new optimal solution. Does the optimal solution change? The extreme point becomes x optimal. The value of the objective function becomes (d) The computer solution for the linear program in part (a) provides the following objective coefficient range information. Variable Objective Coefficient Allowable Increase Allowable Decrease A 3.00000 3.00000 1.00000 B 2.00000 1.00000 1.00000 Use this objective coefficient range information to answer parts (b) and (c). The objective coefficient range for variable A is to . Since the change in part (b) is outside The objective coefficient range for variable B is to . Since the change in part (c) is outside this range, we know the optimal solution will not , vx this range, we know the optimal solution will x change. change