Im having a lot of trouble trying to figure out how to solve this problem, any help is greatly appreciated! Thanks.
The profit (measured in dollars) of a small company has been determined to be
P(x)= 20000 (x / 100 + x^2), where x is the production level (in units).
a) Compute the marginal profit
b) Find the production level xmax that leads to the maximal profit within the range
0 ≤ x ≤ 30.
c) How many dollars of profit does the company make at that production level?
d) Does your answer change if x has to be within the range 0 ≤ x ≤ 10 instead? If yes, how?
June 25th 2010, 01:40 AM
the marginal profit is
maximal profit occurs either at the point where marginal profit = 0, or x=0, or x=30.
Find the profit at each of these points and see which one is higher hintThere is no point in the range 0 < x < 30 where marginal profit =0 in this case.
this is equal to P(x), where x is the production level you found in part b
if your existing answer is in the range 0 < x< 10, then it will not change.
However if your existing answer is not in the range, you need to find a new one, which will be either:
or somewhere in between where the marginal profit is zero (you can discount this possibility as if there was a point in the range with marginal profit =0, you would have found it in part b)
June 25th 2010, 09:07 AM
Thanks so much for your help!
Please let me know if these answers are correct:
d.) No, because in the previous problem, 10 had the highest amount of profit.
June 25th 2010, 11:31 AM
hmm, if i understood your function correctly i dont think you have the marginal profit right
You wrote P(x)= 20000 (x / 100 + x^2)
Did you mean
I'll assume you meant
b) MP = 0 has no solutions where x > 0
So max pforit occurs at either x=0 or x=30
p(0) = 0
p(30) = 1200200