SOLUTION: I'm kinda lost on B Donut Delights, Inc. has determined that when x donuts are made daily, the profit P, in dollars, is given by P(x) = - 0.002 x2 + 4.7x

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Question 1146886: I'm kinda lost on B
Donut Delights, Inc. has determined that when x donuts are made daily, the profit P, in dollars, is given by

P(x) = - 0.002 x2 + 4.7x - 1900

(a) What is the company’s profit if 800 donuts are made daily?
-0.002(800)^2+4.7(800)-1900
-1280+3760-1900 = 580

(b) How many donuts should be made daily in order to maximize the company’s profit? Show work.
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website!
.
On finding the maximum/minimum of a quadratic functions and relevant solved problems read 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
in this site.

A convenient place to observe all these lessons from the "bird flight height" is the last lesson in the list.

Start from the first four lessons.

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.

Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!

I'm kinda lost on B
Donut Delights, Inc. has determined that when x donuts are made daily, the profit P, in dollars, is given by

P(x) = - 0.002 x2 + 4.7x - 1900

(a) What is the company’s profit if 800 donuts are made daily?
-0.002(800)^2+4.7(800)-1900
-1280+3760-1900 = 580

(b) How many donuts should be made daily in order to maximize the company’s profit? Show work.

You're lost on b), not B.
Function:
The MAXIMUM profit occurs where the MAXIMUM number of donuts, or
Now, I'd assume that you know, from the quadratic function, what a, b, and c, are. You just need "a" and "b" here, not "c."
Just substitute those values, "a" and "b," and you should get the number of units/donuts that'll maximize profit.

SOLUTION: I'm kinda lost on B Donut Delights, Inc. has determined that when x donuts are made daily, the profit P, in dollars, is given by P(x) = - 0.002 x2 + 4.7x - 1900