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Suppose that a company estimated that the annual operating cost of its
business delivery van would be $5,000 for insurance plus $0.65 per mile for
gas, oil, and maintenance.
a. What function shows
how total annual
operating cost depends
on number of miles
driven r?
b. Write and solve
equations or inequalities
that match these
questions about the van
operating cost.
i. How many miles can the van be driven if the annual operating cost is to
be less than $15,000?
ii. If the company records show a total operating cost of $20,000 for one
year, how many miles must have been driven with the van?
c. If inflation increases the operating cost of the van at a rate of about 5% per
year and the current annual operating cost is $12,500, what function could
be used to predict the annual operating cost at a time n years later? What
assumption(s) are you making?

Respuesta :

The $5,000 insurance cost and $0.65 maintenance cost per mile gives;

a. Cost, C = 5,000 + 0.65•r

b. i. Lesser than 15,384 mile

ii. 23076.92 miles

c. Annual cost, C, is given by the equation, C = 12,500•(1 + 0.05)^n

How can the cost equations be written?

Insurance cost = $5,000

Cost per mile = $0.65

a. The function for the total annual operating cost, C, is therefore;

  • C = 5,000 + 0.65•r

Where;

r = The number of miles the delivery van has been driven

b. i. When C < 15,000

Therefore;

15,000 < 5,000 + 0.65•r

15,000 - 5,000 = 10,000 < 0.65•r

r = 10,000/0.65 ≈ 15384.6

The number of miles the van can be driven to keep the cost lower than $15,000 is therefore;

  • 15384 miles

ii. When the operating cost is $20,000, we have;

20,000 = 5,000 + 0.65•r

Therefore;

r = 15,000/0.65 ≈ 23076.92

The number of miles driven is approximately 23076.92 miles

c. Current annual cost = $12,500

Inflation rate = 5%

Annual cost in n years is therefore;

C = 12,500•(1 + 0.05)^n

The assumption made is that the inflation rate is applied to cost of each preceding year.

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