Please help with calculus question!

label Calculus
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schedule 1 Day
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A store owner currently sells an item for $50 and can sell 100 items per week on average. However, market research says that for each $3 decrease in price, the owner will be able to sell 25 more items per week. What price should the owner set so that the weekly maximum profit is realized?

Jul 22nd, 2015

Thank you for the opportunity to help you with your question!

Q = 1550/3-25/3*x 

R = PQ = (1550-25x/3*x 

dR/dx = 0 

 1550/3 - 50x/3 = 0 

x = 1550/50 = 31 


 

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 22nd, 2015

What price should the owner set so that the weekly maximum profit is realized? Wouldn't that be 32?

Jul 22nd, 2015

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Jul 22nd, 2015
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Jul 22nd, 2015
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