This question is really to do with how to come to terms with Lagrange multipliers.(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Langrange multiplier with a three constraint problem

Can you offer guidance or do you also need help?

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