Question

An offshore oil well must be connected by pipe to the refinery. The oil-well is 4 km off-shore. The refinery is on the coast, 5 km from the nearest point of land to the oil well. It costs $ S per kilometre 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 ,U and S.

Answer 1

\[\text{cost}\text{ = }S \sqrt{x^2+16}+(U*S)(5-x)\]