Results 1 to 8 of 8

Math Help - Optimization Problem - Part A

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    sydney
    Posts
    4

    Optimization Problem - Part A

    Hi Fellow Maths Friends,

    Going through a problem set and stuck on solving part A of Question 1. Could someone assist and advise if I am on the right track? The figures as I am simplifying seem to be quite large and non elegant. Sorry for the light scan - you may have to highlight page to make darker.

    Thanks heaps for your help.

    Regards,

    math rookie
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: Optimization Problem - Part A

    Hey fagipop.

    For your question is the quantity A, a constant?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2012
    From
    sydney
    Posts
    4

    Re: Optimization Problem - Part A

    Hi Chiro,

    Many thanks for your help. Yes A is to be a constant.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: Optimization Problem - Part A

    So to start you off, turning points in functions occur when you have a minimum or a maximum and when the second derivative is non-zero (it's not a local minimum or a local maximum: you have to check that later on).

    The turning points occur when f'(x) = 0 and a maximum occurs when f''(x) < 0 and a minimum occurs when f''(x) > 0.

    Can you calculate these quantities first?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2012
    From
    sydney
    Posts
    4

    Re: Optimization Problem - Part A

    yes - I have attached my initial attempts in the scan doc - its page 2 onwards behind the question page. I have started by introducing equation Profit = PQ - C (Introduced as Price * Quantity - Cost)
    Variable A and Q have been solved. Is this correct thus far?

    thx
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: Optimization Problem - Part A

    I just noticed you said A was a constant but you are differentiating with respect to A in your answer. Does this mean A is not a constant?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Oct 2012
    From
    sydney
    Posts
    4

    Re: Optimization Problem - Part A

    Sorry - yes you are right. It is not a constant - it has to vary as the number of adverts will constitute to demand variable q.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: Optimization Problem - Part A

    If there are no constraints on your optimization problem, then your approach is good (it doesn't say there are in the question, but it's always a good idea to check).

    If you have constraints, then you need to use what is called Lagrange Multipliers to do the optimization.

    I didn't check the algebra though, but a good way to check these kind of things is to plot the graph (especially around the neighbourhood) to verify that you have a maximum or a minimum. It doesn't mean it is the global maximum or minimum, but it's a way to re-inforce your algebra.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Part of an eigenvector problem...
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: January 16th 2011, 03:49 AM
  2. Replies: 25
    Last Post: January 15th 2010, 03:53 AM
  3. Sum of a part arithmatic and part geometric sequence
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: October 25th 2009, 10:53 PM
  4. Replies: 14
    Last Post: February 13th 2009, 04:27 AM
  5. I need help with the second part of this problem.
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 12th 2007, 03:23 AM

Search Tags


/mathhelpforum @mathhelpforum