Question

Graphically solve the following problem. You need not show me the graph. However, you would need to draw one to solve the problem correctly. You would need to indicate all the corner points clearly. Solve mathematically to identify the intersection points.

Maximize profit = 8 x1 + 5x2   

Subject to   

x1 + x2 <=10
x1 <= 6

x1, x2 >= 0

a. What is the optimal solution?

(You may utilize QM for Windows to answer b to d)
b. Change the right-hand side of constraint 1 to 11 (instead of 10) and resolve the problem. How much did the profit increase as a result of this?

c. Change the right-hand side of constraint 1 to 6 (instead of 10) and resolve the problem. How much did the profit decrease as a result? Looking at the graph, what would happen if the right-hand-side value were to go below 6?

d. Change the right-hand side of constraint 1 to 5 (instead of 10) and resolve the problem. How much did the profit decrease from the original amojnt as a result of this?

e. Examine the following output from QM. What is the dual price of constraint 1? What is the lower bound on this?

Linear Programming Results			Part e
	X1	X2		RHS	Dual
Maximize	8	5
const 1	1	1	<=	10	5
const 2	1	0	<=	6	3
Solution	6	4		68

Ranging

Variable	Value	Reduced	Original Value	Lower Bound	Upper Bound
X1	6	0	8	5	Infinity
X2	4	0	5	0	8
Constraint	Dual Value	Slack/Surplus	Original Value	Lower Bound	Upper Bound
Constraint 1	5	0	10	6	Infinity
Constraint 2	3	0	6	0	10

f. What conclusions can you draw from this regarding bounds of the right-hand-side values and the dual price?

Answer 1