Question 337287: Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.5x^2-0.6x +3.659 where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?
The shop should build ______ bicycles.
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! This may not be the exact answer or correct reason, you can compare the results with other answers.
Solving your quadratic equation using standard formula gives imaginary roots for x.
i.e. x = (0.6 + i2.6) or x = (0.6 - i2.6)
Considering the second requirement, i.e the cost C(x) to be minimum, take first derivative of the equation and evaluate to zero. This gives,
dC(x)/dx = 0.5*2*x - 0.6 = 0
x = 0.6
This means 0.6 * 100 = 60 bicycles.
Verify the result:
For x = 60, C(x) = 1768 dollars. Avg = $29.45
For x = 70, C(x) = 2411 dollars. Avg = $34
For x = 50 or less, the Avg values are lesser than $29.45. I hope this helps.
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