The Auto Company of America (ACA) produces four types of cars: subcompact, compa
ID: 3122014 • 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
a)
As per the given scenario it is difficult solve these problem but i will try to give simple way to find the answers.
I am feeling that these final numbers are with an average fleet MPG of exactly 27.
Now we have to calcullate the Fleet percentgsge and produce for all types as follows,
Type Produce Fleet%
Subcompact 360 0.29999
Compact 260 0.21666
Intermediate 0 0
Luxury 305 0.25416
Truck 275 0.22916
Van 0 0
Now we have to multiply these produce values sum with Profit values sum then the product
value gives the result.
Therefore The optimal annual profit is $375,000 = $375k.
Now we have to multiply MPG values sum with the fleet values sum then we gwt,
Wavg f/e = 26.99
b} If Fuel requirement is raised to 28MPG then we have to lost some profit because when fuel requirement
increases that means the vehicle Km/L decreases so we can say that the performance also secreases.
The profit losses depends on the country, different country vehicles have different Km/L. And also it
has a difference with US(MPG) and Imperial(MPG).
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