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Optimization of 2 eqns

  1. Oct 26, 2011 #1
    1. The problem statement, all variables and given/known data
    I need to optimise a couple of equations.
    I want maximum S for minimum x.

    h, t

    w, j

    2. Relevant equations
    S = ( (j) / (j + 0.5*w) )^2 [Eqn 1]
    x = (const) * (j / w) [Eqn 2]
    [See attachment]

    3. The attempt at a solution
    I've tried to re-arrange [Eqn 1] to make j the subject but I cannot. I get:
    ((j)^2) * ( 1 - S + ((S*w)/j) ) = (S*(w^2))/4

    I thought that if I rearrange both equations for j or w and set them equal to each other then I can try to find the min/max of the equation (for the other variable).

    Any ideas/help please?


    **Edit Oops... posted in the wrong forum sub category. This is not homework nor coursework. This is a personal project. Either way, I could do with some help :-)

    Attached Files:

    Last edited: Oct 26, 2011
  2. jcsd
  3. Oct 26, 2011 #2
    I'm thinking... is it even possible?

    Surely, I can plot S and x over a range of h and w and find where S is maximum and r is minimum??
  4. Oct 26, 2011 #3


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    Homework Helper

    Might be instructive to go through some mental gyrations. For example, assume j is a fixed positive number and figure out what value of w will minimize x or maximize S. Then assume j is a fixed negative number and figure out what value of w will minimize x or maximize S. You should be able to zero in rather quickly on what you are looking for.
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