Question

Can anyone help me with these two optimization problems?

A boat leaves a dock at 9:00 P.M. and travels due south at a speed of 20 km/h. Another boat has been heading due east at 15 km/h and reaches the same dock at 10:00 P.M. How many minutes after 9:00 P.M. were the two boats closest together? Round your answer to the nearest minute.

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 $300,000 per km over land to a point P on the north bank and $600,000 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.)

Answer 1

write the position of each boat as a function of time. Then, write the distance equation between those positions. Then, minimize.

On the second, make a diagram,going up the river L km, then across the river some distance. WRite the cost function as a function of L.