An offshore oil well is 1 mile off the coast. The refinery is 2 miles down the coast. If laying pipe in the ocean is twice as expensive as on land, what path should the pipe follow in order to minimize the cost?
the first thing i did was have X equal the distance from the point of shore closest to the point where the pipe comes ashore. Then the equation
y^2=1^2 + x^2 where y equals the length of pipe
I then had C(x) = 2 sqrt (1 + x^2) + (2 - x)
I took the first derivitave and got
2[x/sqrt (1 + x^2)] - 1
I set this equal to zero and got x = 1/2
I tried plugging this back into my equation C(x) = 2 sqrt (1 + x^2) + (2-x) and I ended up with C = 3.736
My problems are (1) I'm not sure if this is the correct answer and (2) if the math is done right, how does this necessarily answer the question of how the pipe should be laid? Thanks so much.
the first thing i did was have X equal the distance from the point of shore closest to the point where the pipe comes ashore. Then the equation
y^2=1^2 + x^2 where y equals the length of pipe
I then had C(x) = 2 sqrt (1 + x^2) + (2 - x)
I took the first derivitave and got
2[x/sqrt (1 + x^2)] - 1
I set this equal to zero and got x = 1/2
I tried plugging this back into my equation C(x) = 2 sqrt (1 + x^2) + (2-x) and I ended up with C = 3.736
My problems are (1) I'm not sure if this is the correct answer and (2) if the math is done right, how does this necessarily answer the question of how the pipe should be laid? Thanks so much.