1. Consider the following LP problem, in which X and Y denote the number of units of products X and Y to produce, respectively:

Maximize profit = $5X+$5Y

Subject to the constraints

2X+3Y <= 60 (resource 1)

4X+2Y <= 80 (resource 2)

X <= 18 (resource 3)

X, Y >= 0 (nonnegativity)

The Excel Sensitivity Report for this problem is shown below.

Variable Cells

Cell	Name	Final Value	Reduced Cost	Objective Coefficient	Allowable Increase	Allowable Decrease
$B$4	Solution value X	15.00	0.00	5.00	5.00	1.67
$C$4	Solution value Y	10.00	0.00	5.00	2.50	2.50

Constraints

Cell	Name	Final Value	Reduced Cost	Objective Coefficient	Allowable Increase	Allowable Decrease
$D$7	Resource 1	60.00	1.25	60.00	60.00	12.00
$D$8	Resource 2	80.00	0.63	80.00	8.00	40.00
$D$9	Resource 3	15.00	0.00	18.00	1E+30	3.00

Subquestions

Calculate the explain what happens to the optimal solution for each of the following situations. Each question is independent of the other questions.

1. a) What is the optimal solution to this problem?
2. b) For what ranges of values, holding all else constant, could each of the objective function coefficients be changed without changing the optimal solution?
3. c) If we could obtain one additional unit of resource 1, how would it impact profit? Over what range of RHS values could we rely upon this value?
4. d) If we were to give up one unit of resource 2, how would it impact profit? Over what range of RHS values could we rely upon this value?
5. e) If we were to increase the profit for product X by $4, how would the solution change? What would be the new solution values and the new profit?
6. f) If we were to decrease the profit for product Y by $2, how would the solution change? What would be the new solution values and the new profit?
7. g) Suppose that two units of resource 3 were found to be unusable, how would the solution change?
8. h) If we were able to obtain five more units of resource 3, would you be interested in the deal? Why or why not?
9. i) If the profit for product X was increased to $7 while at the same time the profit for product Y was reduced to $4, what would be the new solution values and the new profit?
10. j) Suppose you were to be offered 50 units of resource 1 at a premium of $1 each over the existing cost price for that resource. Would you purchase this? If so, by how much would your profit increase?