Consider the following linear program:

Min 8X+12Y

s.t.

1X+3Y9

2X+2Y10

6X+2Y18

X,Y0

Assume that the objective function coefficient for X changes from 8 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. If required, round your answers to the nearest whole number.

x= ?

y = ?

optimal solution = ?

Assume that the objective function coefficient for X remains 8, but the objective function coefficient for Y changes from 12 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. If required, round your answers to the nearest whole number.

x= ?

y = ?

optimal solution = ?

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 8.000 4.000 4.000

Y 12.000 12.000 4.000

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 that the optimal solution ______________ change.

The objective coefficient range for Y is from _____________ to ______________ so the optimal solution____________ change in part (c) because the new objective coefficient is _______________this range.