1. an oil refinery is located on the north bank of a straight river that is 2 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/km over land to a point p on the north bank and $400,000/km under the river to the tanks. to minimize the cost of the pipeline, how far from the refinery should p be located? (round your answer to two decimal places.)
2. a man launches his boat from point a on a bank of a straight river, 3 km wide, and wants to reach point b, 1 km downstream on the opposite bank, as quickly as possible. he could row his boat directly across the river to point c and then run to b, or he could row directly to b, or he could row to some point d between c and b and then run to b. if he can row 6 km/h and run 8 km/h, where should he land to reach b as soon as possible? (we assume that the speed of the water is negligible compared to the speed at which the man rows.)