.
From the condition, the revenue is
R(x) = x*p = x*(85-0.o0125x) = -0.00125 + 85x thousands of dollars.
It is a quadratic function, and the problem asks you to find its maximum.
For the general form quadratic function y(x) = ax^2 + bx + c with the negative leading coefficient "a"
the maximum is achieved at x = .
In our case, a = 0.0125, b= 85, so the maximum is achieved at
x = = 6800.
It is "the production level that will maximize revenue". ANSWER
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On finding the maximum/minimum of a quadratic function 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
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.