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

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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(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Minimise:
C+=+.009x%5E2+-+1.8x+%2B+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%2F2a
Your equation is already in standard form: C+=+ax%5E2+%2B+bx+%2B+c so here: a = .009 and b = -1.8. The minimum value of C will be found at x+=+-b%2F2a
x+=+-%28-1.8%29%2F2%28.009%29
x+=+1.8%2F.018 Simplify.
x+=+1800%2F18
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%28300%2C200%2C-20%2C200%2C-10%2C120%2C.009x%5E2-1.8x%2B100%29