EXERCISES

$61$

$($a$)$ What is the optimal annual profit for ACA?

$($b$)$ How much would the annual profit drop if the fuel efficiency requirement were raised to $28MPG?$

$2\mathrm{.}7$ Production Planning for Automobiles: The Auto Company of America $($ACA$)$ produces four types of cars: subcompact, compact, intermediate, and luxury. ACA also produces trucks and vans. Vendor capacities limit total production capacity to at most $1,200,000$ vehicles per year. Subcompacts and compacts are built together in a facility with a total annual capacity of $620,000$ cars. Intermediate and luxury cars are produced in another facility with capacity of $400,000$ ; and the truck$/$van facility has a capacity of $275,000.$ ACA's marketing strategy requires that subcompacts and compacts must constitute at least half of the product mix for the four car types. Profit margins, market potential, and fuel efficiencies are summarized below.

$\backslash$table$[[$Type$,\backslash$table$[[$Profit Margin$],[($S$/$Vehicle$)]],\backslash$table$[[$Potential Sales$],[($in $000$s$)]],\backslash$table$[[$Fuel Efficiency$],[($MPG$)]]],[$Subcompact$,150,600,40],[$Compact$,225,400,34],[$Intermediate$,250,300,15],[$Luxury$,500,225,12],[$Truck$,400,325,20],[$Van$,200,100,25]]$

The Corporate Average Fuel Efficiency $($CAFE$)$ standards require an average fleet fuel efficiency of at least $27$ MPG$.$ ACA would like to use a linear programming model to understand the implications of government and corporate policies on its production plans.