Question 3. (20 points) Robin Tires, Inc. makes two types of tires, for SUVs and Hatch- backs. The firm has 500 hours of production time, 250 hours of packaging, and 150 hours available for shipping. The production time required per tire type is given in the following table: Production Hours Production Packaging Shipping Profit/Tire SUV Tires 2 1.5 1 $22 Hatchback Tires 1.5 1 0.5 $12 Type Assume that the company is interested in maximizing the total profit contribution. The sensitivity report provided below was generated using the Excel Solver to determine the optimal solution to this problem. Using the sensitivity report, answer the following: Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $E$3 100 0 22 2 $F$3 0 12 2.666666667 100 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $G$10 150 16 150 16.66666667 25 $G$8 350 0 500 1E+30 150 $G$9 250 4 250 50 25 (a) Optimal production quantity of SUV tires: (b) Optimal production quantity of Hatchback tires: (c) Optimal profit: (d) Will the current optimal solution stay optimal if the unit profit of SUV tires decreases to 19? (Yes or No) (e) Will the current optimal solution stay optimal if we add a constraint that says pro- duction quantity of Hatchback tires should be at most 120? (Yes or No) (f) Calculate the effect on the total profit of increasing the available time for shipping to 160. (g) Calculate the effect on the total profit of decreasing the available time for packaging to 230