Industrial Controls, Inc. (ICI) manufactures two models of a flowmeter used by the thermal power plant to monitor the flow of discharged greenhouse gases. Model A is more accurate than model B. For the next month, the company has orders for 100 units of model A and 150 units of model B. Although ICI purchases all the electronic components used in both models, the plastic cases for both models are manufactured at an ICI plant in Tully, Queensland.

Each model A case requires 4 minutes of injection-moulding time and 6 minutes of assembly time. Each model B case requires 3 minutes of injection-moulding time and 8 minutes of assembly time. For next month, the Tully plant has 600 minutes of injection-moulding time available and 1,080 minutes of assembly time available. The manufacturing cost is $10 per case for model A and $6 per case for model B.

Depending upon demand and the time available at the Tully plant, ICI occasionally purchases cases for one or both models from a third-party supplier to fill customer orders that could not be filled otherwise. The purchase cost is $14 for each model A case and $9 for each model B case. ICIs C-suite wants to develop a minimum cost plan that will determine how many cases of each model should be produced at the Tully plant and how many cases of each model should be purchased.

a. For the optimal solution, how much injection-moulding time is spent?

b. For the optimal solution, how much assembly time is spent?

c. Would the solution change if the injection-moulding time available were only 590 minutes instead of 600 minutes?

d. What would the optimal solution be if the purchase cost for each model B case were increased from $9 to $11?

e. How much would total cost increase or decrease if the assembly time available were 1,100 minutes instead of 1,080 minutes?

please answer all of them if thats possible

The sensitivity analysis report has already been produced as follows. Variable Cells Cell Name $B$9 Model A Manufactured $C$9 Model A Purchased $B$10 Model B Manufactured $C$10 Model B Purchased Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 100 0 10 1.75 1E+30 0 1.75 14 1E+30 1.75 60 0 6 3 2.333333333 90 0 9 2.333333333 3 Constraints 100 Cell Name $B$16 Demand for model A LHS $B$17 Demand for model B LHS $B$18 Injection molding time LHS $B$19 Assembly time LHS Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 100 12.25 100 11.42857143 150 9 150 1E+30 90 ? 0 600 1E+30 20 ? -0.375 1080 53.33333333 480