Consider the following linear program. Min8X+12Ys.t.1X+3Y72X+2Y106X+2Y14X,Y0 (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)=(1) (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,)=() optimal. The value of the objective function becomes Does the optimal solution change? The extreme point (x,Y)=( 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. 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 [ to Since the change in part (b) is this range, we know the optimal solution this range, we know the optimal solution change. change. The objective coefficient range for variable Y is . Since the change in part (c) is this range, we know the optimal solution change