During the next two months an automobile manufacturer must meet (on time) the following demands for trucks and cars: month 1, 400 trucks and 800 cars; month 2, 300 trucks and 300 cars. During each month at most 1000 vehicles can be produced. Each truck uses two tons of steel, and each car uses one ton of steel. During month 1, steel costs $700 per ton; during month 2, steel is projected to cost $800 per ton. At most 2500 tons of steel can be purchased each month. (Steel can be used only during the month in which it is purchased.) At the beginning of month 1, 100 trucks and 200 cars are in the inventory. At the end of each month, a holding cost of $200 per vehicle is assessed. Each car gets 35 miles per gallon (mpg), and each truck gets 15 mpg. During each month, the vehicles produced by the company must average at least 23 mpg. a. Determine how to meet the demand and mileage requirements at minimum total cost. b. Use SolverTable to see how sensitive the total cost is to the 23 mpg requirement. Specifically, let this requirement vary from 20 mpg to 30 mpg in increments of 0.5 mpg. Explain intuitively what happens when the requirement is greater than 27 mpg.
During the next two months an automobile manufacturer must meet (on time) the following demands for trucks and cars: month 1, 400 trucks and 800 cars; month 2, 300 trucks and 300 cars. During each month at most 1000 vehicles can be produced. Each truck uses two tons of steel, and each car uses one ton of steel. During month 1, steel costs $700 per ton; during month 2, steel is projected to cost $800 per ton. At most 2500 tons of steel can be purchased each month. (Steel can be used only during the month in which it is purchased.) At the beginning of month 1, 100 trucks and 200 cars are in the inventory. At the end of each month, a holding cost of $200 per vehicle is assessed. Each car gets 35 miles per gallon (mpg), and each truck gets 15 mpg. During each month, the vehicles produced by the company must average at least 23 mpg. a. Determine how to meet the demand and mileage requirements at minimum total cost. b. Use SolverTable to see how sensitive the total cost is to the 23 mpg requirement. Specifically, let this requirement vary from 20 mpg to 30 mpg in increments of 0.5 mpg. Explain intuitively what happens when the requirement is greater than 27 mpg.
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