SOLUTION: the cost of operating a testing device for n minutes is given by C(n) = 1.4n^2 - 35n + 270 find the number of minutes the device had to be operated to minimize the cost? wha

Question 173716: the cost of operating a testing device for n minutes is given by
C(n) = 1.4n^2 - 35n + 270
find the number of minutes the device had to be operated to minimize the cost?
what is the minimum cost?

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
C(n) = 1.4n^2 - 35n + 270
.
This is a parabola in standard form. Since the 'a' coefficient (1.4) is positive, finding the vertex will give you the minimum.
The n coordinate = -b/2a
-(-35)/2(1.4)
(35)/(2.8)
12.5
.
find the number of minutes the device had to be operated to minimize the cost?
12.5 minutes
.
what is the minimum cost?
To find the cost, stuff n=12.5 into the cost equation:
C(n) = 1.4n^2 - 35n + 270
C(12.5) = 1.4(12.5)^2 - 35(12.5) + 270
C(12.5) = 218.75 - 437.5 + 270
C(12.5) = $51.25

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