# Math Help - Optimization Problem

1. ## Optimization Problem

I'm really confused on this problem[GVIDEO][/GVIDEO]

A company wishes to run a utility cable from point A on the shore to an installation at point B on the island. The island is 6 miles from the shore (point O) It costs $3000 per mile to run the cable on land and$5000 per mile underwater. Assume that the cable starts at A and runs along the shoreline, then angles and runs underwater to the island. Let x represent the distance from O at which the underwater portion of the cable begins, and the distance between A and O be 9 miles.

1. Write the total cost C as a function of x.
2.Find the point at which the line should begin to angle in order to minimize the total cost.
3. what is the minimum cost?

2. You want to find where to put point P so that
$3000 * length of AP +$5000 * length of PB is a minimum.