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! :)
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.