Consider the following linear program. Min 8X + 12Y s.t. 1X + 3Y 2X + 2Y > 14 6X + 2Y > 18 X, Y 20 (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.) 10 9 Fill No Solution Help WebAssign. Graphing Tool What is the value of the objective function at the optimal solution? X at (X, Y) = (b) Assume that the objective function coefficient for X changes from 8 to 6. 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.) No Solution Help Fill WebAssign. Graphing Tool Does the optimal solution change? ---Select--- remains becomes becomes x optimal. The value of the objective function becomes The extreme point x (C) Assume that the objective function coefficient for X remains 8, but the objective function coefficient for Y changes from 12 to 6. 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.) 10 >> Fill NO Solution Helg WebAssign. Graphing Tool Does the optimal solution change? The extreme point 2,3 becomes optimal. The value of the objective function becomes 34 X. x (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 X 8.00000 4.00000 4.00000 Y 12.00000 12.00000 4.00000 How would this objective coefficient range information help you answer parts (b) and (c) prior to re-solving the problem? this range, we know the optimal solution will not change. The objective coefficient range for variable Y is to The objective coefficient range for variable X is Since the change in part (C) is outside . Since the change in part (b) is within this range, we know the optimal solution will change