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The Auto Company of America (ACA) produces four types of cars: subcompact, compa

ID: 3121977 • Letter: T

Question

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.

Type

Profit margin ($/vehicle)

Potential sales (in 000s)

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.

Using excel and the solver tool:

1) What is the optimal annual profit for ACA?

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

Type

Profit margin ($/vehicle)

Potential sales (in 000s)

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

Explanation / Answer

Type Profit margin ($/vehicle) Potential sales (in 000s) Fuel efficiency (MPG) MADE MAX CAN BE MADE PRODUCE FLEET % Subcompact 150 600 40 620 620 0.0 7.12413E-07 Compact 225 400 34 161 400 620.0 0.587119788 Intermediate 250 300 15 275 275 0.0 0 Luxury 500 225 12 1056.00128 1200 161.0 0.152463149 Truck 400 325 20 275.0 0.26041608 Van 200 100 25 0.0 2.70604E-07 TOTAL PROFIT 330000.5267 CAP MPG 26.99998744