An oil refinery is located on the north bank of a straight river that is 1 km wide.?

A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 3 km east of the refinery. The cost of laying pipe is $200,000 per km over land to a point P on the north bank and $400,000 per km under the river to the tanks. To minimize the cost of the pipeline, how far from the refinery should P be located? (Give your answer correct to two decimal places.)

w = width of river

you need to minimize function (3-a)*200000 + sqrt(a^2+w^2)*400000 in terms of a (take derivative, find zeroes and so on)