Question

An oil well at O is in the ocean, 8 miles from T on a straight shoreline.
The oil has to go from O to R. the cost of laying pipe per mile is $90,000 underwater and $54,000 on land. the cheapest method of placing the pipe is to lay OP underwater and PR on land, where P is some point on RT. What is the amount of money that CAN BE Saved by using this method instead of going directly from O to R underwater?


using optimazatio can you please help me, I have no idea how to solve this problem.

Answer 1

There are many variations of this same question,.

Hint: let TP = x
then OP^2 = x^2 + 64
OP = (x^2 + 64)^(1/2)

I think you are missing the length of TR, we need that to find PR
Just for arguments sake, lets say TR = 12 miles
then PR = 12-x

cost = 90000(x^2+64)^(1/2) + 54000(12-x)
take the derivative, set that equal to zero and solve for x

Change the 12 miles to whatever you question has