A cable is to be run from a power plant on one side of a river 900 meters wide t
ID: 2831615 • Letter: A
Question
A cable is to be run from a power plant on one side of a river 900 meters wide to a factory on the other side, 3000 meters downstream. The cable will be run in a straight line from the pwoer plant to some point on the opposite bank and ten along the bank to the factory. The cost of running the cable across the water is 5.00 per meter, while the cost of running it over land is 4.00 per meter. let x be the distance from p to the point directly across the river from the power plant. express the cost of installing the cable as a function of x.
Explanation / Answer
A classic problem and one of my favorites!
Cost = 4x + 5?(900^2 + (3000 - x)^2)
Drawing the graph, I find the most economical route is 1800 m downstream over the water, then 1200 m over the land.
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