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Modeling Capital and Operating Cost
To decide when to replace company cars, an accountant looks at two cost components: capital cost and operating cost. The capital cost is the difference between the original cost and the salvage value, and the operating cost is the cost of operating the vehicle.
a) For a new Ford Fusion, the capital cost is $3000 plus $0.12 for each mile that the car is driven. Write the capital cost C as a function of the number of miles the car is driven x.
b) If a Ford Fusion is purchased for $19,846 and driven 80,000 miles, then what is its salvage value?
c) The operating cost P for the Fusion starts at $0.15 per mile when the car is new and increases linearly to $0.25 per mile when the car reaches 100,000 miles. Write P as a function of x.
d) What is the operating cost at 70.000 miles?
e) The total cost per mile is given by . Identify all asymptotes and graph T as a function of x.
f) Explain each asymptote in terms of this application.
g) Find T for x = 20.000, 30.000, and 90.000 miles.
h) The senior vice president has told the accountant that the goal is to keep the total operating cost less than $0.38 per mile. Is this goal practical?
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College Algebra (6th Edition)
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