In this video a brief discussion about multivariable function with constraint is given followed by comprehensive explanation of soving the same with Lagrangian Multiplier method
for more numerical example on same topic follow the link:
https://www.youtube.com/watch?v=IKGdqZ-XdoI&list=PLEpoNV0nW_dfx8wr2J4pVVpoYSocyD6-A&index=13
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Lagrangian Multiplier Method | Optimization of Multivariable function subjected to constraint | NatokHD