Question
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
a. 1.00
b. 0.43
c. 0.00
d. 2.00
e. 1.44
Answers
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?
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?
I will try but there is no diagram.
The solution for x does fit one of the answers. So the interpretation should be correct.
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