SOLUTION: Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.1x^2-0.5x+6.47, where C(x) is in hundreds of dollars. H

Algebra ->  Radicals -> SOLUTION: Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.1x^2-0.5x+6.47, where C(x) is in hundreds of dollars. H      Log On


   



Question 397091: Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.1x^2-0.5x+6.47, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycles.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
C%28x%29=0.1x%5E2-0.5x%2B6.47
To make math easier, I'm going to say D%28x%29+=+100%2AC%28x%29
so, D%28x%29 will be in dollars
D%28x%29+=+10x%5E2+-+50x+%2B+647
In a quadratic equation the minimum occurs at x+=++-b%2F%282a%29
where the equation is of the form
ax%5E2+%2B+bx+%2B+c
-b%2F%282a%29+=+50%2F20
50%2F20+=+5%2F2
D%28x%29+=+10%285%2F2%29%5E2+-+50%2A%285%2F2%29+%2B+647
D%28x%29+=+250%2F4+-+250%2F2+%2B+647
D%28x%29+=+-250%2F4+%2B+2588%2F4
D%28x%29+=+2338%2F4
D%28x%29+=+584.5 dollars
250 bikes must be made to minimize cost at $584.50