Pipeline Calculus Question

Question

An offshore oil well is 3 kilometers off the coast. The refinery is 4 kilometers down the coast (see figure). Laying pipe in the ocean is twice as expensive as on land. What path should the pipe follow in order to minimize the cost? X= ? km

Answer 1

The length of the ocean pipe is x² + 9.

Its cost is 2x² + 18.

The land pipe costs 4 - x.

The combined cost is 2x² - x + 22

For what value of x is that at a minimum?