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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:

 

https://math.stackexchange.com/questions/2801275/finding-the-firms-maximum-monthly-profit ]

 

Thank you in advance! :)

 May 30, 2018
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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

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