The Big Motor Works (BMW) is considering a production schedule for cars and trucks over the next two months. They must deliver on time 400 trucks and 800 cars in month one. In month two, their demand is 300 trucks and 300 cars. During each month, at most 1,000 vehicles can be built. Each truck uses two tons of steel and each car uses one ton of steel. During the first month, the steel cost will be $400 per ton. During the second month the cost of steel will go up to $600 per ton. At most 2,500 tons of steel can be purchased in each month. (Steel can only be used in the month it is purchased.) At the beginning of month one, 100 trucks and 200 cars are in inventory. At the beginning of each month a hold- ing cost of $150 per vehicle is assessed. Each car gets 30 mpg, and each truck gets 20 mpg. To meet fuel economy regulations, the vehicles produced each month must average at least 26 mpg. The company wants to minimize its total costs. a. Formulate a linear program to help BMW determine how many cars and trucks it should produce each month and how many it should keep in inventory each month. b. Use Solver to find the optimal solution to the linear program from part a. Using a sensitivity report from the Solver solution in part b, answer questions c-g. c. How many trucks and how many cars should be produced in each month? d. Suppose the price of steel fell by $25 per ton. What would be the total impact on optimal solution and optimal value? e. The company just got notified the supply of steel has decreased from 2,500 tons to 2,000 tons. What impact will this have on their production plans? f. The company is able to add overtime at a cost of $900 per car to increase total production in either month. Should they add overtime in either month? Why or why not? The Big Motor Works (BMW) is considering a production schedule for cars and trucks over the next two months. They must deliver on time 400 trucks and 800 cars in month one. In month two, their demand is 300 trucks and 300 cars. During each month, at most 1,000 vehicles can be built. Each truck uses two tons of steel and each car uses one ton of steel. During the first month, the steel cost will be $400 per ton. During the second month the cost of steel will go up to $600 per ton. At most 2,500 tons of steel can be purchased in each month. (Steel can only be used in the month it is purchased.) At the beginning of month one, 100 trucks and 200 cars are in inventory. At the beginning of each month a hold- ing cost of $150 per vehicle is assessed. Each car gets 30 mpg, and each truck gets 20 mpg. To meet fuel economy regulations, the vehicles produced each month must average at least 26 mpg. The company wants to minimize its total costs. a. Formulate a linear program to help BMW determine how many cars and trucks it should produce each month and how many it should keep in inventory each month. b. Use Solver to find the optimal solution to the linear program from part a. Using a sensitivity report from the Solver solution in part b, answer questions c-g. c. How many trucks and how many cars should be produced in each month? d. Suppose the price of steel fell by $25 per ton. What would be the total impact on optimal solution and optimal value? e. The company just got notified the supply of steel has decreased from 2,500 tons to 2,000 tons. What impact will this have on their production plans? f. The company is able to add overtime at a cost of $900 per car to increase total production in either month. Should they add overtime in either month? Why or why not