A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
An electronics store sells an average of 60 entertainment systems per month at an average of $800 more than the cost price. For every $20 increase in the selling price, the store sells one fewer system. What amount over the cost price will maximize revenue?
 2 years ago
An electronics store sells an average of 60 entertainment systems per month at an average of $800 more than the cost price. For every $20 increase in the selling price, the store sells one fewer system. What amount over the cost price will maximize revenue?

This Question is Closed

jayz657
 2 years ago
Best ResponseYou've already chosen the best response.0c = cost price s = selling price n = number of systems sn = total revenue sn  c = income/profit/loss s = (c+800) n = 60 c? if s goes up 20 n = n 1 sorry this is all i got so far, hope it helps in any way

Algebraic!
 2 years ago
Best ResponseYou've already chosen the best response.0Q = 60 + (800P)/20 R= QP = (100 P/20)P so find the max of R = P^2 /20 +100P and find the Price at that max... (set the derivative equal to zero and solve for P)

apple_pi
 2 years ago
Best ResponseYou've already chosen the best response.1First thing you want is number sold in terms of price sold at lets call number sold n, and price sold p \[n = 60\frac{p800}{20}\] \[n = 60+\frac{800p}{20}\] revenue (r) = number sold x price sold \[r = p(60+\frac{800p}{20})\] \[r = 60p+40p\frac{p^2}{20}\] \[r = 100p  \frac{p^2}{20}\] To find the max, we find the stationary point (we know since this is a quadratic, and that the coefficient of p^2 is negative the max is the stationary point) \[\frac{dr}{dp} = 100 \frac{2p}{20}\] \[\frac{dr}{dp} = 100 \frac{p}{10}\] \[0 = 100  \frac{p}{10}\] \[0 = 1000  p] \[p = 1000]

ivano_logy
 2 years ago
Best ResponseYou've already chosen the best response.0Thank you very much! I finally understand it.
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.