Chapter 1.6, Problem LC

LINKING

concepts... For Individual or Group Explorations

Minimizing Construction Cost

A homeowner needs to run a new water pipe from his house to a water terminal as shown in the accompanying diagram. The terminal is 30 ft down the 10–ft-wide driveway and on the other side. A contractor charges $ 3/ft alongside the driveway and $4/ ftfor underneath the driveway.

a) What will it cost if the contractor runs the pipe entirely under the driveway along the diagonal of the 30–ft by 10–ft rectangle?

b) What will it cost if the contractor runs the pipe 30 ft alongside the driveway and then 10 ft straight across?

c) The contractor claims that he can do the job for $120 by going alongside the driveway for some distance and then going under the drive diagonally to the terminal. Find x. the distance alongside the driveway.

d) Write the cost as a function of x and sketch the graph of the function.

e) Use the minimum feature of a graphing calculator to find the approximate value for x that will minimize the cost.

f) What is the minimum cost (to the nearest cent) for which the job can be done?