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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 7 km east of the refinery. The cost of laying pipe is $400,000/km over land to a point P on the north bank and $800,000/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.)

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To minimize the cost, we take the straight distance from the refinery to the other side of the river as 2 km. Also, the 7 km will be the distance that has to be traveled by the pipeline in land. The total cost, C, is therefore,
               total cost =   (2 km)($800,000/km) + (7 km)($400,000 /km)
                    total cost = $4,400,000
Thus, the total cost of the pipeline is approximately $4,400,000.00. 
 

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