Question

Dayton Power and Light, Inc., has a power plant on the Miami Riverwhere the river is 800 ft wide. To lay a new cable from the plantto a location in the city 2 mi downstream on the opposite sidecosts $180 per foot across the river and $100 per foot along theland.
(a) Suppose that the cable goes from the plant to a point Q on theopposite side that is x ft from the point P directly opposite theplant. Write a function C(x) that gives the cost of laying thecable in terms of the distance x.
(b) Generate a table of values to determin if the least expensivelocation for point Q is less than 2000 ft or greater than 2000 ftfrom point P.

Answer 1

First lets put the two distances the cable will cover in terms of x:

The length on the ground is 2 miles minus x. to find c weneed to use the pythagorean theorem:
\(\displaystyle{800}^{{2}}+{x}^{{2}}={c}^{{2}}\)
\(\displaystyle{c}=\sqrt{{{800}^{{2}}-{x}^{{2}}}}\)
now we have all the information we need to make a costfunction:
\(\displaystyle{C}{\left({x}\right)}={180}\sqrt{{{800}^{{2}}-{x}^{{2}}}}+{100}{\left({10560}-{x}\right)}\)
b) use point plotting to answer b