I want to know that can all of the lagrange multipliers can be non zero at the same time. I have a problem with two variables and three constraints. I solved the problem for all possible combinations of the multipliers i.e all multipliers are zero, one zero and two non zero, two zero and one non zero and finally all zeros. I come with some conclusions for all cases but for the last when all are non zero i have two first order gradient equations and three unknown multipliers. so do i have infinite solutions or it interprents something different??please help
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1The Lagrange multipliers needn't be zero. – Nov 30 '16 at 11:07
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It is not possible to help if you do not provide any details. State the problem at least. – A.Γ. Nov 30 '16 at 11:22