SOLUTION: http://imgur.com/oQHUMnL Here is picture in case I copied wrong. ^^ I also found a the question similarly answered on yahoo but got confused with how the answer came about ht

Algebra ->  Finance -> SOLUTION: http://imgur.com/oQHUMnL Here is picture in case I copied wrong. ^^ I also found a the question similarly answered on yahoo but got confused with how the answer came about ht      Log On


   

Question 970356: http://imgur.com/oQHUMnL
Here is picture in case I copied wrong. ^^
I also found a the question similarly answered on yahoo but got confused with how the answer came about https://answers.yahoo.com/question/index?qid=20120419061530AAW2vsZ



The total profit $P, generated from the production and marketing of n items of a certain product is given by
P = −62400 n−8 n^3+1800 n^2−132
How many items should be made for maximum profit? What is the maximum profit?
Enter your answers as a list [in square brackets] of the form: [ n, p]
for some number of items n and profit p (in dollars, but don't include the dollar sign).

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The total profit $P, generated from the production and marketing of n items of a certain product is given by
P+=-62400n-8n%5E3%2B1800n%5E2-132
How many items should be made for maximum profit? What is the maximum profit?
Enter your answers as a list [in square brackets] of the form: [+n,+p]
for some number of items n and profit p (in dollars, but don't include the dollar sign).
P+=-62400n-8n%5E3%2B1800n%5E2-132...rearrange the terms
P+=+-8n%5E3%2B1800n%5E2-62400n-132+
dP%28n%29%2Fdn+=-24n%5E2%2B3600n-62400
dP%28n%29%2Fdn+=-24n%5E2%2B3600n-62400
dP%28n%29%2Fdn+=-24%28n%5E2-150n%2B2600%29
dP%28n%29%2Fdn+=-24%28n%5E2-150n%2B2600%29
dP%28n%29%2Fdn+=-24%28n%5E2-130n-20n%2B2600%29
dP%28n%29%2Fdn+=-24%28%28n%5E2-130n%29-%2820n-2600%29%29
dP%28n%29%2Fdn+=-24%28n%28n-130%29-20%28n-130%29%29+
dP%28n%29%2Fdn+=-24+%28n-20%29+%28n-130%29
-24+%28n-20%29+%28n-130%29=0=> if n=20 or n=130
Which of these is the maximum?
if n=20
p+=+-8%2A20%5E3%2B1800%2A20%5E2-62400%2A20-132
p+=+-592132
if n=130
p+=+-8%2A130%5E3%2B1800%2A130%5E2-62400%2A130-132
p+=+4731868
the maximum profit is at n+=+130
the maximum profit is P=4731868
answer is:
[130, 4731868]