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Langrange multiplier with a three constraint problem

  1. Feb 24, 2008 #1
    This question is really to do with how to come to terms with Lagrange multipliers.

    I have uploaded a jpeg file with this question. The parameters for the question are as below:


    Cost functions of the two generators. C1 = 0.6X1 C2 = 0.8X2

    Demand constraint X1 + X2 = 300

    Generator constraints 0 ≤ X1≤ 200
    0 ≤ X2≤ 200

    minimise π = 0.6X1 + 0.8X2

    The graph below shows in green lines various values of π. The minimisation equation is rewritten as
    X1 = (π - 0.8X2)/0.6. The slope of the graph is then -0.8/0.6. The green lines are then for various parameters of π(pi).
    My question is how does grad(π) come up with correct answer of X1 = 200; X2=100.
    How does this point come out to be the right point
     

    Attached Files:

  2. jcsd
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