min 8X + 12Y

1X + 3Y > or = 10

2X + 2Y > or = 10

6X + 2Y > or = 18

X,Y > or = 0

a. Use the graphical solution procedure to the 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 constraint 2?