SOLUTION: 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

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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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