Question 1162430: A textile manufacturer makes blankets and sells them for $25 each. The cost, in dollars, of making x blankets is given by the formula: Cost=c(x)=5000+4x+0.001x^2.
Find the number of blankets that the manufacturer should produce in order to maximize its profit.
Answer by VFBundy(438)   (Show Source):
You can put this solution on YOUR website! The cost is 
The sale price is 
Therefore, the profit is 
Simplify the profit:
= 
To find the maximum profit, use the equation  , where b = 21 and a = -0.001.
=  =  = 10500
The maximum profit is reached when the manufacturer makes 10,500 blankets.
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Check it:
When the manufacturer makes 10,500 blankets, the profit is:
=  = 105250.
When the manufacturer makes 10,499 blankets, the profit is:
=  = 105249.999
When the manufacturer makes 10,501 blankets, the profit is:
=  = 105249.999
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