I am in a sticky situation at the moment involving a min/max calculus problem.
the problem goes as follows.
An offshore oil well must be connected by pipe to the refinery. The oil-well is 3 km off-shore. The refinery is on the coast, 6 km from the nearest point of land to the oil well. It costs $ S per kilometer to lay pipe along the shore, but U times as much per km to lay pipe underwater. The pipe may be laid either straight to the refinery or to an intermediate point on the coast then along the coast.
Give the total cost as a function of the distance x between the point directly opposite the oil well and the place where the pipe comes ashore. This should be a formula involving x, S and U.
Now I have considered a right angled triangle with U length on one side and S on the other and x being the hypotenuse. Now with that being the case, x^2 = u^2 + s^2 so x = sqrt(u^2 + s^2) with 0 < u < 3 and 0 < s < 6.
However the question says cost as a function of the distance x between the point directly opposite the oil well and the place where the pipe comes ashore. This is the bit Iím struggling to comprehend. Any help would be greatly appreciated!