Calc Word Problem... Need Help!

I have been trying to figure out this problem. I have the answers in the back of the book and saw an attempt of it online, and still am not understanding what was done.

The question says: Supertankers off-load oil at a docking facility 4 miles offshore. The nearest refinery is 9 miles east of the shore point nearest the docking facility. A pipeline must be constructed connecting the docking facility with the refinery. The pipeline costs 300,000 per mile if constructed underwater and 200,000 if over lands.

a) Locate point B to minimize the cost of construction. (Point B forms a triangle with the docking station and point A)

b) The cost of underwater construction is expected to increase whereas the cost of overland construction is expected to stay constant. At what cost does it become optimal to construct the pipeline directly to point A)

If someone could help me with this problem that would be great. Thanks!

I can get you set up.

The key is to let x be the distance from A to B. Then the rest of the shore distance is 9-x.

The distance from B to the facility is the hypotenuse of the triangle.
Use Phy. Th. to get the underwater distance given by sqrt(x^2+16). Thus the cost of underwater pipe is 300,000*(sqrt(x^2+16)). The shore pipe cost is then simply 200,000*(9-x)

So total cost is: 300,000*(sqrt(x^2+16)) + 200,000(9-x) in dollars.

You need to take the derivative and set equal to zero to find the optimum point x. This requires some algebra and squaring both sides. This is the answer to part a).

The rest of the problem I leave to you.