1. ## Optimisation Problem

Hey guys, I having some problems with a math question for my uni homework and would greatly appreciate any assistance
A company wishes to construct a pipeline connecting an oil refinery to an offshore drilling platform. The platform is situated 12km down the shore from the refinery and 11km out to sea. Constructing a pipeline in the ocean is more expensive than the one on land, so the company wants to run part of the pipeline along the shore and part of it through the ocean. The problem is to find the length of the pipeline along the shore which minimises the cost.
1) Find expressions for the length of the pipeline along the shore and in the water in terms of the angle the pipeline makes with shore, theta
2) What is the appropriate range of values that theta can have in this problem?
3) It costs $60K per km to construct a pipeline on land and$120K per km to construct a pipeline in water. Write down an expression for the total cost (in thousands) to build the pipeline in terms of theta
4) Find the value of theta that gives the minimum cost.
5) Find the length of the land and water that minimise the cost and the cost itself.
Cheers, any help would be greatly appreciated.

2. ## Re: Optimisation Problem

Hey rjd871.

Hint: If the shore is approximately straight then you are going to have a right angle triangle with the right angle being the angle between the side of the "shore" portion of the piping and the side that connects the point of the drilling section to the nearest point on the shore.