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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Langrange multiplier with a three constraint problem

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**