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I have the question "A Gas Outlet is one one side of a river 120 m wide. It is exactly 300 meters downstream and across the river from a cottage. A gas line is to be constructed to join the outlet to the cottage. Underwater, the cost is 13 dollars per meter while on land it is 5 dollars per meter. Determine the length of a line that should be laid on land to minimize the cost of the construction of the pipeline".

I am unsure about how to solve this, I have looked at similar questions and could not find a solution to how I would solve this.

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You have one variable to choose, $d$, which is how far downstream the pipe goes while passing under the river. From that, you need to go $300-d$ downstream and $180$ crosswise on dry land and $d$ downstream and $120$ crosswise underwater. Compute the total cost, take the derivative with respect to $d$, set to zero, ...

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  • $\begingroup$ I didn't quite get your answer, what would the total cost formula be? I can take the derivative but I still don't get what the formula that I take the derivative of would be. $\endgroup$ – maldahleh Jan 24 '16 at 4:43
  • $\begingroup$ You need to figure the straight line lengths on land and underwater, multiply each by the cost per meter, and add them. That gives the total cost. $\endgroup$ – Ross Millikan Jan 24 '16 at 4:48

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