# Math Help - Profit Function

1. ## Profit Function

Been going back and forth and just want to see if I've come to the right conclusion! (Also if this is in the wrong section, let me know. New on here!)
Question:
Fixed costs of 10, Average Variable Cost function of q2+4 and the demand equation is p+q=20.

A)Determine the profit function in terms of q.
C(x)= q2+4+10
=q2+14

p(x) - p=20-q
R(x) = [20-q][q]
=20q-q2
Therefore P(x) = 20q-q2-q2+14
= -2q2+20q+14

B) Determine the production level that maximises the profit.

= -b/2(a)
= -20/2(-2)
= 5

2. ## Re: Profit Function

Originally Posted by simon24
Been going back and forth and just want to see if I've come to the right conclusion! (Also if this is in the wrong section, let me know. New on here!)
Question:
Fixed costs of 10, Average Variable Cost function of q2+4 and the demand equation is p+q=20.

A)Determine the profit function in terms of q.
C(x)= q2+4+10
=q2+14

p(x) - p=20-q
R(x) = [20-q][q]
=20q-q2
Therefore P(x) = 20q-q2-q2+14
= -2q2+20q+14
Yes, this is correct.

B) Determine the production level that maximises the profit.

= -b/2(a)
= -20/2(-2)
= 6
Well, that's just bad arithmetic! 20/4 is NOT 6.

3. ## Re: Profit Function

Originally Posted by HallsofIvy
Yes, this is correct.

Well, that's just bad arithmetic! 20/4 is NOT 6.
Oh man me and my typing skills. I did have 5 written down! That's what I get for doing this quickly. Anyway thanks for checking the first part as well!