Question 3. Linear Optimization (12 points) The BlueSky Auto Company (BSAC) produces four types of gasoline-based cars: subcompact, compact, intermediate and luxury. They also produce electric trucks and vans. Due to capacity limit, BSAC can make at most 1.2 million vehicles per year. Subcompacts and compacts are made in one facility with a total annual capacity of 620,000 cars. Intermediate and luxury cars are product in another facility with capacity of 400,000 units; and the electric truck/van facility has a capacity of 275,000. BSAC's management team requires that subcompacts and compacts must constitute at least half of the product mix for the four gasoline-based cars. Also, the management wants to have at least 40% total vehicles are electric. The Corporate Average Fuel Economy (CAFE) standards in the Energy Policy and Conservation Act require an average fuel economy of at least 28 mpg for the gasoline-powered fleet. Profit margins, market demand potential, and fuel efficiencies are summarized as follows: Vehicle Type Power Capacity Limit Profit Margin Maximum Fuel Efficiency Source (units in '000) ($/vehicle) Market (mpg) Demand (units in '000) Subcompact Gasoline 620 150 600 40 Compact Gasoline 225 100 34 Intermediate Gasoline 400 250 300 15 Luxury Gasoline 500 225 12 Truck Electric 275 400 325 20 Van Electric 200 100 25 Question 3.1 (7 points) In the space below, write out the mathematical formulation of the optimization problem if BSAC wants to maximize its annual profit. Please clearly define the decision variables, express the objective as a function, and show all necessary constraints Question 3.2 (3 points) Implement the above optimization model in Excel. Question 3.3 (2 points) Use Analytic Solver or Excel Solver to solve the above optimization problem. How many gasoline- powered cars and how many electric cars should BSAC make to maximize its annual profit? Round to whole numbers. Answers: # of gasoline-powered cars: # of electric cars