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. What is the value of the objective function at the optimal solution? at (X,Y)= 49 (0,7) (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. Does the optimal solution change? The extreme point (X,Y)= 5,5 The extreme point (X, Y) = Variable (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. Does the optimal solution change? X X Y 8.00000 (d) The computer solution for the linear program in partxa) provides the following objective coefficient range Information. Objective Allowable Allowable Coefficient Increase Decrease 12.00000 X 4.00000 remains optimal. The value of the objective function becomes 30 12.00000 -Select- 4.00000 4.00000 optimal. The value of the objective function becomes 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 objective coefficient range for variable Y is to to X Since the change in part (b) is-Select- this range, we know the optimal solution -Select- change. The Since the change in part (c) is-Select- this range, we know the optimal solution -Select- change.

Ment+1241x+3r72x+2y186x+2r14xy0 x,n,n=(x) solution is Slece the change in part () a this range; we know ite upcrial satheon. Isvas the change in part (c) a crange. The objestive coefficant range tor varable r is to