Consider below the linear programming problem:

Max 3A+2B

s.t.

1A+1B≤10

3A+1B≤24

1A+2B≤16

A, B≥0

 

Constraint	Constraint R.H. side	Allowable increase	Allowable decrease
1	10	1.20	2
2	24	6	6
3	16	Infinite	3

The value of the optimal solution is 27. Suppose that the right-hand side for consraint1 is increased from 10 to 11.

• Use the graphical solution procedure to find the new optimal solution. 
• Use the solution to part (a) to determine the shadow price for constraint 1.

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

• 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 0.5. Using this shadow price and the right-hand-side range information in part (c), what conclusion can you draw about the effect of changes to the right-hand side of constraint 2?