Homework Help: calculus

Posted by Angel on Thursday, September 22, 2011 at 8:02am.

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 - MathMate, Thursday, September 22, 2011 at 9:04am
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 - Angel, Thursday, September 22, 2011 at 9:14am
I will try but there is no diagram.
calculus - MathMate, Thursday, September 22, 2011 at 8:04pm
The solution for x does fit one of the answers. So the interpretation should be correct.

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