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 36c/(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? Use the methods outlined in this section to find the minimum.

x= ? mi

Question

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 36c/(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? Use the methods outlined in this section to find the minimum.

x= ? mi

anonymous · Answer

Are you familiar with differential calculus?  If you are, take the first derivative of y = f(x) = cx + 36c/(x + 1) .

anonymous · Answer

so would that be, c+ (-36c/(x^2 + 2x +1))

anonymous · Answer

Yes, and just set that = 0

anonymous · Answer

You will get a value for x that will contain an expression for "c".

anonymous · Answer

5c/6  and -7c/6 ?

anonymous · Answer

problem out to an intermediate step and it looks like the "c" cancels.  It boils down to finding the zeros for x^2 + 2x - 35 = 0.  Find the x value that gives the minimum.

anonymous · Answer

c=0?

anonymous · Answer

oh ok, it's 5! thanks so much!!

anonymous · Answer

You're welcome!