During the next two months an automobile manufacturer must meet (on time) the following demands fortrucks and cars: month 1, 400 trucks and 800 cars;month 2, 300 trucks and 300 cars. During each monthat most 1000 vehicles can be produced. Each truckuses two tons of steel, and each car uses one ton ofsteel. During month 1, steel costs $700 per ton;during month 2, steel is projected to cost $800 perton. At most 2500 tons of steel can be purchased eachmonth. (Steel can be used only during the month inwhich it is purchased.) At the beginning of month 1,100 trucks and 200 cars are in the inventory. At theend of each month, a holding cost of $200 per vehicleis assessed. Each car gets 20 miles per gallon (mpg),and each truck gets 10 mpg. During each month, thevehicles produced by the company must average atleast 16 mpg.a. Determine how to meet the demand and mileagerequirements at minimum total cost.b. Use SolverTable to see how sensitive the total costis to the 16 mpg requirement. Specifically, let thisrequirement vary from 14 mpg to 18 mpg in increments of 0.25 mpg. Explain intuitively what happenswhen the requirement is greater than 17 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 20 miles per gallon (mpg),
and each truck gets 10 mpg. During each month, the
vehicles produced by the company must average at
least 16 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 16 mpg requirement. Specifically, let this
requirement vary from 14 mpg to 18 mpg in increments of 0.25 mpg. Explain intuitively what happens
when the requirement is greater than 17 mpg.
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