You have solved a maximization problem with 4 variables and 3 constraints and have printed out the following sensitivity report:

Microsoft Excel 16.0 Sensitivity Report Worksheet: [ass1.xlsx]Q2 Report Created: 18/09/2020 11:48:15 AM

Answer the following questions (you can assume that all the constraints are of type):

1. Does the solution have multiple optimal solutions? Provide a short explanation.

2. What is the optimal objective function value if the RHS value of the first constraint increases to 60? Provide a short explanation.

3. What is the optimal objective function value if the RHS value of the second constraint decreases to 40? Provide a short explanation.

4. What is the optimal objective function value if the RHS value of the third constraint increases to 50? Provide a short explanation.

5. Assume that new technology has been introduced to our production system and that producing product 2 (X2) now requires the use of 2 units less of resource 1 (Constraint 2) and 1 unit less of resource 3 (Constraint 3) compared to current practice (the use of resource 2 has not changed). Would the optimal solution be different after this new technology is introduced? Provide a short explanation.

Microsoft Excel 16.0 Sensitivity Report Worksheet: [ass1.xlsx]Q2 Report Created: 18/09/2020 11:48:15 AM Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $C$7 X1 2 0 5 1.4375 1.6875 $D$7 X2 0 -3.4875 4 3.4875 1E+30 $E$7 X3 8 0 7 2.090909091 4.6 $F$7 X4 3 0 6 2.7 0.766666667 Constraints Final Shadow Constraint Allowable Cell Name Value Price R.H. Side Increase $G$12 LHS 40 1.4375 40 24 $G$13 LHS 47 0.3375 47 24 $G$14 LHS 37 0.2875 37 10 Allowable Decrease 25.6 10 8