SOLUTION: Maximum cost using the quadratic equations, functions, inequalities and their graphs. It costs Acme Manufacturing C dollars per hour to operate its golf ball division. An analyst

Question 23274: Maximum cost using the quadratic equations, functions, inequalities and their graphs. It costs Acme Manufacturing C dollars per hour to operate its golf ball division. An analyst has determined that C is related to the number of golf balls produced per hour, x, by the equation C = 0.009x^2 - 1.8x + 100. What number of balls per hour should Acme produce to minimize the cost per hour of manufacturing these golf balls?
Answer by Earlsdon(6098) (Show Source):
You can put this solution on YOUR website!
Minimise:

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:
Your equation is already in standard form: so here: a = .009 and b = -1.8. The minimum value of C will be found at

Simplify.

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: