a) (20 pts) Write the optimal solution and objective function value.

b) (20 pts) Determine the objective function value when we increased the unit of resource of 3 from 24 to 28. Can you find the new optimal solution X1 and X2? Explain.

c) Determine the objective function value if the profit of x1 is increased from 35 to 40? Does the solution change? Explain.

d) Determine the objective function value if the profit of x2 is decreased from 30 to 25? What can you say about the solution? Explain.

e) Determine the objective function value when we increased the unit of resource of 1 from 16 to 20. What can you say about the solution? Explain.

Figure I provides the Excel Sensitivity output for the following LP model. Max Z- 35x1 + 30x2 subject to X: +2x 516 XI + x 59 3x + 2x2 5 24 X,X > 0 Variable Cells Final Reduced Objective Allowable Allowable Cel Name Value Cost Coefficient Increase Decrease $B$10 Solution X1 6 0 35 10 5 $C$10 Solution X2 3 0 30 5 6.666666667 Constraints Cel Name $D$4 Constrant 1 $D$5 Constrant 2 $D$6 Constrant 3 Figure 1 Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 12 0 16 1E+30 9 20 9 1 1 24 5 24 3