Question 414284
{{{C(x) = .1x^2 - .2x + 3.511}}}
You want to find the vertex of this curve
It's in the form
{{{y = a*x^2 + b*x + c}}}
The vertex is at V(x,y) where {{{x = -b/(2a)}}}
{{{-b/(2a) = -(-.2)/(2*.1)}}}
{{{-b/(2a) = .2/.2}}}
{{{-b/(2a) = 1}}}
and
{{{C(1) = .1*1^2 - .2*1 + 3.511}}}
{{{C(1) = .1 - .2 + 3.511}}}
{{{C(1) = 3.411}}}
They should build 100 bicycles to minimize cost, which would be $341.10 per bicycle
Here's a plot (in hundreds of dollars and hundreds of bicycles)
{{{ graph( 400, 400, -.5, 10, -.5, 10,  .1x^2 - .2x + 3.511) }}}