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# Finding the Firm's Maximum Monthly Profit?

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So I've been stuck on this question for a while, and I tried asking others and googling it. However, I still don't understand as to how I can get the right answer. It's a lenghty question, and I already asked on another math forum, so I'm just gonna post it here:

Thank you in advance! :)

May 30, 2018

### 1+0 Answers

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Equate the marginal revenues to marginal costs and solve for x.

5000 -20x =300 + 1/4x^2, solve for x

x = ~103 items sold.

Revenues =5000x - 10x^2

=5000*103 - 10* 103^2

=515,000 - 106,090

=\$408,910 - total revenues for 1 month.

Total costs =300x + 1/12x^2

=30,900 + 884.08

=\$31,784.08 - total costs for 1 month.

Total revenues - Total costs =\$408,910 - \$31,784.08 =\$377,125.92 - The firm's maximum monthly profit.

May 30, 2018