The cost of laying cable

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Question from Gilligan, a student:

MetroMedia cable is asked to provide service to a customer whose house is located 2 miles from the road along which the cable is buried.
The nearest connection box for the cable is located 5 miles down the road. If the installation cost is 10 dollars per mile along the road and 14 dollars per miles off the road, express the total cost C of installation as a function of the distance x (in miles) from the connection box to the point where the cable installation turns off the road. Give the domain.

Also, compute the cost if x = 1 mile and if x = 3 miles.

In order to use the given values for x, do I need a formula?

If so, what is that formula?

I can take it from there.

Hi Gilligan.

If the distance the cable is laid along the road is x and the distance in the road-wise direction between the connexion box and the house is 5 miles, then the road-wise length of off-road cabling is 5 - x.

So you have a right triangle for the off-road portion where the cable is laid along the hypotenuse and the lengths of the two legs of the right triangle are 2 and 5 - x. Use Pythagorus to find the length of the hypotenuse in terms of x. Multiply by 14. That's the offroad cost. Add that to 10x for the onroad cost. That's your function.

Hope this helps,
Stephen La Rocque.

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.