Maximize profit = $5X + $5Y Subject to the constraints: 2X3Y60 (Resource 1) 4X2Y80 (Resource 2) X 18 (Resource 3) X,Y 0 (nonnegativity) The Excel Sensitivity Report for this problem is shown in the below. Calculate and explain what happens to the optimal solution for each of the following situations. Each question is independent of the other questions. Variable Cells Final Cell Name Value Reduced Objective Allowable Allowable Cost Coefficient Increase 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 Final Shadow Cell Name Value $D$7 Resource 1 60.00 Price 1.25 Constraint Allowable Allowable R.H. Side Increase Decrease 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 (1) What is the optimal solution to this problem? (3 pts) (2) For what ranges of values, holding all else constant, could each of the objective function coefficients be changed without changing the optimal solution? (4 pts) (3) 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? (3 pts) (4) 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? (3 pts) (5) 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? (2 pts) (6) 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? (2 pts) (7) Suppose that two units of resource 3 were found to be unusable, how would the solution change? (2 pts) (8) If we were able to obtain five more units of resource 3, would you be interested in the deal? Why or why not? (2 pts) (9) 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? (4 pts)