calculus

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A power station is on one side of a river that is 0.5 mile wide, and a factory is 5.00 miles downstream on the other side of the river. It costs $15 per foot to run overland power lines and $23 per foot to run underwater power lines. Estimate the value of x that minimizes the cost.


a. 1.00

b. 0.43

c. 0.00

d. 2.00

e. 1.44

  • calculus -

    The question did not define x, which is probably shown in a diagram.

    Let us define x as the distance downstream of the power station across the river, to which point the under-river power line connects.

    Then the cost function
    C(x)=15*(5-x)+23*sqrt(0.5^2+x^2)
    You need to minimize C(x) with respect to x.
    Can you take it from here?

  • calculus -

    I will try but there is no diagram.

  • calculus -

    The solution for x does fit one of the answers. So the interpretation should be correct.

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