SOLUTION: suppose that the manufacturer of a dvd player has found that, when the unit price is p dollars, the revenue r (in dollars) as a function of the price p is r(p)=-2.5p^2+800p. (a)

Question 1115177: suppose that the manufacturer of a dvd player has found that, when the unit price is p dollars, the revenue r (in dollars) as a function of the price p is r(p)=-2.5p^2+800p.
(a) for what price will the revenue be maximized?
(b) what is the maximum revenue?
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.

The revenue will be maximized when the quadratic function 


r(p) = =-2.5p^2 + 800p 


will get the maximum.


It will happen when  p =  =  = 160 dollars.


It is optimal price for dvd player.


And the maximum revenue then will be  then  -2.5*160^2 + 800*160 = 64000 dollars.

----------------
On finding the maximum/minimum of a quadratic function see the lessons in this site
    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Finding minimum/maximum of quadratic functions".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

RELATED QUESTIONS
suppose that the manufacturer of a dvd player has found that, when the unit price is p... (answered by josmiceli)

Suppose that the manufacturer of a DVD player has found that, when the unit price... (answered by Boreal)

Solve the problem. The manufacturer of a CD player has found that the revenue R (in... (answered by stanbon,josgarithmetic)

Maximizing Revenue Suppose that the manufacturer of a gas clothes dryer has found that,... (answered by rapaljer)

Suppose that the manufacturer of a gas clothes dryer has found that, when the unit (answered by josmiceli)

Manufacturer of a clothes dryer has found that, when the unit price is p dollars, the... (answered by scott8148)

(Revenue) The John Deere company has found that the revenue from sales of heavy-duty... (answered by stanbon)

The car company has found that the revenue from sales of sedans is a function of the unit (answered by Alex.33,ikleyn)

The marketing department at the John Deere company has found that the revenue from the... (answered by solver91311)