SOLUTION: If P(x) =5+8x-5x^2 represents the profit in selling x thousand Boombotix speakers, how many speakers should be sold to maximize profit?

Question 1100684: If P(x) =5+8x-5x^2 represents the profit in selling x thousand Boombotix speakers, how many speakers should be sold to maximize profit?
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!

The x-value of the peak ( max profit ) is:

----------------

800 speakers should be sold
------------------------------
check:
Here's the plot
Plug back into equation to get

Answer by ikleyn(52812)   (Show Source): You can put this solution on YOUR website!
.
The core knowledge for solving such problems IS THIS

If you are given a quadratic function y = ax^2 + bx + c, then it gets its maximum/minimum at x= .

In your case, a= -5, b= 8 and c= -5, so the maximum is achieved at x = = of thousand = 800 speakers.

To read and learn more about this subject, see the lessons
    - 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

    - A rectangle with a given perimeter which has the maximal area is a square

    - A farmer planning to fence a rectangular garden to enclose the maximal area
    - A farmer planning to fence a rectangular area along the river to enclose the maximal area
    - A rancher planning to fence two adjacent rectangular corrals to enclose the maximal area
    - Using quadratic functions to solve problems on maximizing revenue/profit

    - OVERVIEW of lessons on finding the maximum/minimum of a quadratic function

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.

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