# Oil Refinery: Optimization Problem

1. Sep 27, 2009

### sobek

1. The problem statement, all variables and given/known data

A drilling rig 12 miles off shore is to be connected by a pipe to a refinery onshore, 20 miles down the coast from the rig. If underwater pipe costs $40,000 per mile and land based pipe costs$30,000 per mile what value of x and y would give the least expensive connection?

3. The attempt at a solution

I have no idea on where to start. I know I need to find a relevant equation, differentiate it, then set it to 0, and finally show that it is a relative minimum, but I'm having trouble finding the relevant equation. I recreated the image that was in my textbook, and attached it to this post.

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2. Sep 27, 2009

### Bohrok

First replace x with an expression that has y, using the Pythagorean theorem, so you have to work with just one variable.

The land distance will be 20-y miles and the land pipe costs $30,000 per mile, so the cost for land pipe will be$30,000(20-y). Find another expression like that for the underwater pipe cost, then add the two to get a function of y for the cost.