What is the Maximum Profit for a Firm with a Given Profit Curve?

[ditchqueen]

I Think I am right on a, but not quite sure on B. I put this in the calc section, because I think B needs to be solved as a dirivitive.
Thank you

Given a firms profit curve of:
Profit= -3 + 15Q - 1.25Q^2
a) Calculate the output that would maximize the firms's profit.

15-1.25Q^2=0
15=1.25
15/1.25 = 12
Output = 12


b)Calculate the maximum profit:
-3 + 15Q-1.25Q^2
-3 +15 (12) - 1.25 (24)=
57-30=27

 

[Hootenanny]

Hi ditchqueen and welcome to the forums.

On question (a) you have the right idea, but you haven't differentiated correctly, check the final term. As for (b) you have answered this correctly, except you have used the incorrect values from question (a). Also note that $12^2\neq24$.

 

[ditchqueen]

Lost

I think I am lost on the differentiated part. I can't believe I had 12^2 as 24! I know better then that sorry :)
Ok I think I did it! Is the dir 0?

 

[HallsofIvy]

I Think I am right on a, but not quite sure on B. I put this in the calc section, because I think B needs to be solved as a dirivitive.

Actually, it is A that requires the derivative

Thank you

Given a firms profit curve of:
Profit= -3 + 15Q - 1.25Q^2
a) Calculate the output that would maximize the firms's profit.

15-1.25Q^2=0

The derivative of -3+ 15Q- 1.25Q² is 15- 2(1.25)Q= 15- 2.5Q

15=1.25
15/1.25 = 12
Output = 12

15- 2.5Q= 0 so 2.5Q= 15. Q= 15(2/5)= 6

b)Calculate the maximum profit:
-3 + 15Q-1.25Q^2
-3 +15 (12) - 1.25 (24)=
57-30=27

Q= 6, not 24.

 

[ditchqueen]

Thank you! I have some questions though
-3+ 15Q- 1.25Q2 is 15- 2(1.25)Q= 15- 2.5Q
What happened to the -3? also , is it 2(1.25) because the Q was squared?
Thank you