Question 2 - 16 Marks

Consider the following linear program:

Min 8X + 12Y

s.t.

1X + 3Y 9

2X + 2Y 10

6X + 2Y 18

X, Y 0

Suppose that the right-hand side for constraint 1 is increased from 9 to 10.

Use the graphical solution procedure to find the optimal solution.

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

The sensitivity report for the linear program in this question provides the following right- hand-side range information:

Constraint Constraint

RH 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?

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?