SOLUTION: I need help figuring out the following quadratic word problem, I am totally confused by this problem. Minimum Cost: It costs Acme Manufacturing C dollars per hour to operate

Question 23660: I need help figuring out the following quadratic word problem, I am totally confused by this problem.
Minimum Cost:
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?
Any help or explanation will be greatly appreciated.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
C = 0.009x^2 - 1.8x + 100
COMBINE X^2 AND X TERMS TO FIT A PERFECT SQUARE
C=0.1{0.09X^2-18X}+100
C=0.1{(0.3X)^2-2*(0.3X)*30+30^2-30^2}+100
C=0.1{(0.3X-30)^2}+100-90
C=0.1{(0.3X-30)^2}+10
HENC C WILL BE MINIMUM IF {(0.3X-30)^2}IS MINIMUM WHICH BEING PERFECT SQUARE WILL BE MINIMUM ZERO WHEN 0.3X=30...OR...X=30/0.3=300/3=100...THAT IS WHEN 100 BALLS ARE MADE PER HOUR....THE MINIMUM COST IS C=10...
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