Average cost of a bicycle is modeled by the function c(x)=.1x^2-1.7x+10 where c(x) is measured in dollars. how many bicycles should be built in order to minimize the average cost per bicycle?
To find the number of bicycles that should be built in order to minimize the average cost per bicycle, we need to find the minimum point of the function c(x) = 0.1x^2 - 1.7x + 10.
To find the minimum point, we can use calculus. The minimum point occurs when the derivative of the function is zero.
1. Take the derivative of c(x) with respect to x:
c'(x) = 0.2x - 1.7
2. Set c'(x) = 0 and solve for x:
0.2x - 1.7 = 0
0.2x = 1.7
x = 1.7 / 0.2
x = 8.5
Therefore, the minimum point occurs at x = 8.5.
Since we are dealing with the number of bicycles, which is a discrete value, we need to round the answer to the nearest whole number.
Therefore, the suggested number of bicycles to be built in order to minimize the average cost per bicycle is approximately 9.