SOLUTION: Say that a business determines its profit function is: P ( x ) = x^2 - 6 x + 1 where X is the number of units produced in thousands and P ( x ) is the profit made in thousands of

Question 1127391: Say that a business determines its profit function is: P ( x ) = x^2 - 6 x + 1 where X is the number of units produced in thousands and P ( x ) is the profit made in thousands of dollars.
Does this mean that the business should produce 3,000 units to maximize its profit
Found 3 solutions by josmiceli, stanbon, ikleyn:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Yes, but the equation should be:

in order for the peak to be a maximum
and for to be positive when
is a maximum

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Say that a business determines its profit function is: P ( x ) = x^2 - 6 x + 1 where X is the number of units produced in thousands and P ( x ) is the profit made in thousands of dollars.
Does this mean that the business should produce 3,000 units to maximize its profit
----
Max profit occurs when x = -b/(2a) = 6/2 = 3
----
Answer: Yes
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Cheers,
Stan H.
Answer by ikleyn(52775)   (Show Source): You can put this solution on YOUR website!
.

Say that a business determines its profit function is: P ( x ) = x^2 - 6 x + 1 where X is the number of units
produced in thousands and P ( x ) is the profit made in thousands of dollars.

Does this mean that the business should produce 3,000 units to maximize its profit
~~~~~~~~~~~~~~~~~~~

Let me make couple of notices:

1. The given quadratic function has a MINIMUM at x= 3 thousands. 2. The given quadratic function HAS NO a MAXIMUM at x= 3 thousands.

Therefore, the question is IRRELEVANT to the given part.

Not only irrelevant - it CONTRADICTS to the given part.

Have a nice evening / night / morning / day .

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

If you want to learn the basics on minimum and maximum of quadratic functions,
two groups of lessons were developed in this site specially for you :

    - 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 (*)

A convenient place to observe all these lessons from the "bird flight height" is the last lesson in the list, marked by (*).

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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