Please answer the question fully (parts a-d).

Consider the following linear program. Min 8X + 12Y s.t. 1X + 3Y 27 2X + 2Y 2 10 6X + 2Y 2 14 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 Graph Layers Segment 1 Segment 2 Segment 3 No Solution Help IClowAll 9 Jo x X X What is the value of the objective function at the optimal solution? 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.) 10 Graph Layers After you add an object to the graph you can use Graph Layers to view and edit its properties. No Solution Help S Fill 9 7 6 5 3 2 Does the optimal solution change? The extreme point -Select- optimal. The value of the objective function becomes (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 Graph Layers 9 After you add an object to the graph you can use Graph Layers to view and edit its properties. 7 No Solution Help B 5 4 3 2 Does the optimal solution change? The extreme point --Select-- 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 Allowable Coefficient 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? The objective coefficient range for variable X is range, we know the optimal solution --Select--- change. The objective coefficient range for variable Y is to . Since the change in part (b) is ---Select-- this to . Since the change in part (c) is ---Select--- this range, we know the optimal solution --Select--- change