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A woman wishes to rent a house within 9 miles of her work. If she lives x miles from her work, her transportation cost will be cx dollars per year, while her rent will be 4c x 1 dollars per year, where c is a constant taking various situational factors into account. How far should she live from work to minimize her combined expenses for rent and transportation

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Answer:

Combined cost C(x) = cx + 4c/(x+1)

minimum C(x) ==> C '(x) = 0

==> c - 4c/(x+1)2 = 0

==> 4c/(x+1)2 = c

==> (x+1)2 = 4

==> x +1 = 2

==> x = 1 mile

Hence she should live 1 mile from work to minimise comined costs.

Step-by-step explanation:

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