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Math Help - At what quantity is the total revenue maximised?

  1. #1
    abc
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    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?


    All i think about this question is to change it to 32-Q^2, then i
    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.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by abc View Post
    A firm has a demand function P = 32 – Q
    At what quantity is the total revenue maximised?


    All i think about this question is to change it to 32-Q^2, then i
    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
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  3. #3
    abc
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    so if i use PQ=32Q-Q^2. can i use quadratic formual to find Q. But would this give me the maximum aswell.
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    Grand Panjandrum
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    Quote Originally Posted by abc View Post
    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
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  5. #5
    abc
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    Quote Originally Posted by CaptainBlack View Post
    The maximum of this quadratic is midway between its roots.

    RonL
    Okay thanks so which formula do i use do find it.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by abc View Post
    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
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  7. #7
    abc
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    Quote Originally Posted by Jhevon View Post
    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.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by abc View Post
    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
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  9. #9
    abc
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    Quote Originally Posted by Jhevon View Post
    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.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by abc View Post
    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"
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