Consider the following linear program.

Max	3A	+	2B
s.t.
	1A	+	1B		10
	3A	+	1B		27
	1A	+	2B		18
	A,	B	0

The value of the optimal solution is 28.5. Suppose that the right-hand side for constraint 1 is increased from 10 to 11.

(a)

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

What is the value of the objective function at the optimal solution?

---------- at (A, B) = ( ----------)

(b)

Use the solution to part (a) to determine the dual value for constraint 1.

----------

(c)

The computer solution for the linear program provides the following right-hand side range information.

Constraint	RHS Value	Allowable Increase	Allowable Decrease
1	10.00000	2.60000	1.00000
2	27.00000	3.00000	13.00000
3	18.00000	Infinite	6.50000

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

The range for constraint 1 is ---------- . As long as the right-hand side stays ---Select--- within outside ---------- this range, the dual value of ---------- is applicable.

(d)

The dual value for constraint 2 is 0.5. Using this dual value 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?

The value of the optimal solution will increase by ---------- for every unit increase in the right-hand side of constraint 2 as long as the right-hand side is ---Select--- within outside ---------- the range ---------- to ---------- .