See the attached files.
C(q) = 0.000002q^3 - o.o117q^2 + 84.446q + 23879
R(q) = -0.00003 * q^3 +0.0495q^2 + 118.02q
P(q) = -0.000032q^3 + 0.0612q^2 + 33.554q - 23879
Use the Cost, Revenue, and Profit functions to find. a) C`(q) b) R`(q) c) P`(q) Do these equations predict the quantity needed to maximize profit, and the amount? Explain your answer fully. (Please see Lab5student (attached) for information associated with answering my problem, which is lab 6, also attached). Thank you.
I found the derivatives :
C`(q)= .000006q^2 - .0234q + 84.446
R`(q)= -.00009q^2 + .099q + 118.02
P`(q)= -.000096q^2 + .1224q + 33.554
But, I don't know where to go from here. Do I set C'(q) = R'(q) to get max profit? I don't understand how to do the second part of the question, even assuming that I found the derivatives correctly.
The solution is attached below (next to the paperclip icon) in two formats. one is in Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.
The slope of the tangential line to the profit function at the maximum point is ...
This solution is comprised of a detailed explanation to solve derivative problem.