4. Consider the linear program in problem 3. The value of the optimal solution is 48. Suppose the right-hand side for constraint 1 is increased from 9 to 10.

(problem 3 linear program)

Min 8X+12Y s.t.

1X+3Y9

2X+2Y10

6X+2Y18

A,B0

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:

Constriant	RHS values	Allowable Increase	Allowable Decrease
1	9.00000	2.00000	4.00000
2	10.00000	8.00000	1.00000
3	18.00000	4.00000	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 constraint 2?

Please show the steps to solving the problem. Thank you.