Please provide steps

. Consider the following linear program:

Min 8X + 12y

s.t.

1X + 3y> 9

2X + 2y>10

6X + 2y>18

X, y > 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 sensitivity report 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 resolving the problem?

Problem 4 (8 points)

Consider the linear program in Problem 3. The value of the optimal solution is 48. Sup- pose that the right-hand side for constraint 1 is increased from 9 to 10.

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

b. Use the solution to part (a) to determine the shadow price for constraint 1.

c. The sensitivity report for the linear program in Problem 3 provides the following right- hand-side range information:

Constraint	Constraint R.h. Side	Allowable Increase	Allowable Decrease
1	9,000	2.000	4,000
2	10,000	8,000	1,000
3	18,000	4,000	Infinite

What does the right-hand-side range information for constraint 1 tell you about the shadow price for constraint 1?

d. The shadow price for constraint 2 is 3. Using this shadow price and the right-hand- side range information in part (c), what conclusion can be drawn about the effect of changes to the right-hand side of constrain 2?