# Thread: At what quantity is the total revenue maximised?

1. ## At what quantity is the total revenue maximised?

A firm has a demand function P = 32 – Q
At what quantity is the total revenue maximised?

think you have to find the derivative but it doesn't make sense to
me still.

If you could give me a hint on what i need to look for that would be
great.

I would really appreciate your help.

2. Originally Posted by abc
A firm has a demand function P = 32 – Q
At what quantity is the total revenue maximised?

think you have to find the derivative but it doesn't make sense to
me still.

If you could give me a hint on what i need to look for that would be
great.

I would really appreciate your help.
P is the unit price, so the total revenue is PQ=32Q-Q^2.

RonL

3. so if i use PQ=32Q-Q^2. can i use quadratic formual to find Q. But would this give me the maximum aswell.

4. Originally Posted by abc
so if i use PQ=32Q-Q^2. can i use quadratic formual to find Q. But would this give me the maximum aswell.
The maximum of this quadratic is midway between its roots.

RonL

5. Originally Posted by CaptainBlack
The maximum of this quadratic is midway between its roots.

RonL
Okay thanks so which formula do i use do find it.

6. Originally Posted by abc
Okay thanks so which formula do i use do find it.
finding the roots is one way (which we can do by factoring or the quadratic formula or completing the square ...) but it's easier to just find the vertex directly. we can do this through completing the square or by using the vertex formula.

Vertex formula:

The vertex for a quadratic of the form $y = ax^2 + bx + c$ occurs when:

$x = \frac {-b}{2a}$

Completing the square:

we complete the square to get the quadratic in the form: $y = a(x - h)^2 + k$

when in this form, the vertex is given by: $(h,k)$

here, the x-value is your Q

7. Originally Posted by Jhevon
finding the roots is one way (which we can do by factoring or the quadratic formula or completing the square ...) but it's easier to just find the vertex directly. we can do this through completing the square or by using the vertex formula.

Vertex formula:

The vertex for a quadratic of the form $y = ax^2 + bx + c$ occurs when:

$x = \frac {-b}{2a}$

Completing the square:

we complete the square to get the quadratic in the form: $y = a(x - h)^2 + k$

when in this form, the vertex is given by: $(h,k)$

here, the x-value is your Q
thanks i no how to use the vertex formula but i still don't get your post. Basically if i put in the values into the vertex formula then i will get a value. what do i do next.

8. Originally Posted by abc
thanks i no how to use the vertex formula but i still don't get your post. Basically if i put in the values into the vertex formula then i will get a value. what do i do next.
the value you get will be the Q that maximizes the revenue. once you have that, you just do what the question asks. the question asked for the Q that maximizes revenue, so you're done

9. Originally Posted by Jhevon
the value you get will be the Q that maximizes the revenue. once you have that, you just do what the question asks. the question asked for the Q that maximizes revenue, so you're done
Oh okay so just to double check if i put the values in the vertic formula it would be -32/(2*-1), so Q is 16.

10. Originally Posted by abc
Oh okay so just to double check if i put the values in the vertic formula it would be -32/(2*-1), so Q is 16.
yes

and it's "vertex"