Question 23274
Minimise:
{{{C = .009x^2 - 1.8x + 100}}}

This is the equation of a parabola that opens upwards (Coefficient of x^2 is positive), so the minimum value of C would be at the parabola's vertex.  The x-coordintate of the vertex is given by: {{{x = -b/2a}}}

Your equation is already in standard form: {{{C = ax^2 + bx + c}}} so here: a = .009 and b = -1.8.  The minimum value of C will be found at {{{x = -b/2a}}}

{{{x = -(-1.8)/2(.009)}}}
{{{x = 1.8/.018}}} Simplify.
{{{x = 1800/18}}}
{{{x = 100}}}

Acme should produce 100 ball per hour to minimise the cost per hour.

It might be helpful to see the graph of the cost, C (vertical axis) versus x (horizontal axis) the number of balls produced:

{{{graph(300,200,-20,200,-10,120,.009x^2-1.8x+100)}}}