Lagrange multiplier example: Minimizing a function subject to a constraint

I discuss and solve a simple problem through the method of Lagrange multipliers. A function is required to be minimized subject to a constraint equation. Such an example is seen in 2nd-year university mathematics.

Category:

Education

Tags:

• Lagrange
• multipiers
• Multivariable
• calculus
• MATH2019
• Dr
• Chris
• Tisdell
• UNSW
• Sydney
• Engineering
• Mathematics

[H60hadgi]

I thought you always ADDED the Lambda(constraint) to the objective function? you have it as being subtracted. Does it not matter because you are essentially adding or subtracting zero?

[DrChrisTisdell]

@H60hadgi It doesn't matter. The reason goes back to the proof of the Lagrange method (that is, why it works). The idea is that at points of max/min there is a number lambda such that grad f = lambda (grad g), that is, the two vector grad f and grad g are parallel, so you could write it as grad f = - lambda (grad g) instead and this still accurately says that the two vectors are parallel.

[YumiKondo0911]

Thank you very much for this lecture! What if there are additional inequality constraint x>=0,y>=0,z>=0, how can we use lagrange method??

[DrChrisTisdell]

@YumiKondo0911 If you add those extra constraints to this example then there is no solution.  Can you see why?

[KillerChaijBalin]

thats an easy example, can u show some more dificult ones? related to the part where we need to be "creative".

[DrChrisTisdell]

@KillerChaijBalin /watch?v=mFTNEkFveaY and start at 20:39

[guitfan33]

I LOVE LAGRANGE!!!

[zululu2222]

thanks . 

[gusphol]

Mr Tisdale, Thank you for making this video.

[leoncio91]

awesome video, thanks!

[success2508]

THANKS...IT HELP ME VERY MUCH TO UNDERSTAND

[success2508]

THANK YOU VERY MUCH  RESPECTED SIR.