Consider the following linear program: Min 8x +12y s.t. 1x + 3y > o

Consider the following linear program:

Min 8x +12y

s.t.

1x + 3y > or equal to 9

2x + 2y > or equal to 10

6x + 2y > or equal to18

AB > or equal to 0

a) Use the graphical solution procedure to find the optimal solution.

b) 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.

c) 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.

d) The sensivitiy report for the linear program in part (a) provides the following objective coefficient range information:

VARIABLE OBJECTIVE COEFFICIENT ALLOWABLE INCREASE ALLOWABLE DECREASE

x 8000 4000 4000

y 12000 12000 4000

How would this coefficient range information help you answer parts (b) and (c) prior to resolving the problem?