Lagrange multiplier example: Minimizing a function subject to a constraint

[zululu2222]

thanks . 

[gusphol]

Mr Tisdale, Thank you for making this video.

[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?

[leoncio91]

awesome video, thanks!

[success2508]

THANKS...IT HELP ME VERY MUCH TO UNDERSTAND

[success2508]

THANK YOU VERY MUCH  RESPECTED SIR.

[guitfan33]

I LOVE LAGRANGE!!!

[pinkythongT]

THANKS!!!

[GEORGEBELG]

Thank you so much Chris, I do enjoy watching your online lectures and the way you manage to pass your mathematics knowledge to the audience (for me this demonstates a talented teacher). Once again, this video is an excellence piece of work!

George

[DrChrisTisdell]

@GEORGEBELG Thanks for taking the time to give feedback, George!

[1990maverickhunter]

Your video has helped me a lot. You have my thanks.

[Changer01]

I think this will help my understanding of in mathematic methods of physical chemistry a LOT.

[kathysoiio]

*****!

btw thanks!

[arunthiagarajah]

Thanks so much for this tutorial I wish my Maths lecturer was as good as you!

[kstahmer]

Thank you Dr. Tisdell.

Your video is an excellent tutorial for beginners, and people like me, who learned Lagrange Multipliers four decades ago, had fuzzy recollections about them and are suddenly confronted with a pragmatic problem, where their use is indispensible.

Intuitively, Lagrange Multipliers simplify many problems, since partial derivatives reduce the power of unknowns by 1 and eliminate constants. This linearizes a problem's higher degree equations.

[presidentevil]

you don't have to use lagrange multiplier for this. You can find z as a function of x and y in the constraint equation, take partial of f with respect to x and y, set both equal to zero and find all the points that are correct.

If you have more than one constraint then maybe you can do this.

[DrChrisTisdell]

Dear presidentevil - yes, that's true.

Many problems in mathematics have a variety of solution methods.

Thanks for commenting.

Chris

[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

[mzjocker]

wow you're a life saver :] thanks for posting your videos!

[metainfinity]

Thanks, this was helpful.

[DrChrisTisdell]

You're welcome.

[aryanmit3754]

sir could u please tell hw to optimise a non linear equation subjected to inequatilities

[ataylor0002]

Hi! Hopefully you will read this before my Vector Calculus exam on Friday! Can you help me setting up this question please

A metal gas cylinder is made up of a sheet of cylindrical metal (which both ends open) and two hemispherical caps made of a different type of metal. If the metal from the cap costs twice as much per square metre than the sheet of the cylinder, what is the ratio of length to radius for the cylindrical part that minimses the cost for a given total volume of the container?

[ulivaldo]

Thank you, very simple but explains clearle what is plain and how to get distances from the origin

[DrChrisTisdell]

You're welcome. Thanks for posting.

[phatinc]

Thanks Dr Tisdell, your narration to the question is very clear and I especially love the part where you read my mind when I thought to myself "What happened to the dL/dlambda?".

This will undoubtedly help in my 2019 test tomorrow :D

[DrChrisTisdell]

Good luck with the test phatinc. Make sure you have looked at those sample tests that I posted on My eLearning a few weeks back.

Never really thought of myself as a mindreader! :-)

[phatinc]

Just finishing the last question of the last sample paper right now...with a bit of procrastinating...

Again, thanks for all the help. I wish I had you for maths1A, would of made things a lot easier and more interesting.

[sidis4uonly]

Thanks Doctor. Its very handy to have such kind of virtual teacher. this video is very helpful. thanks heaps. :)

[DrChrisTisdell]

No worries, Sidis!! Thanks for the feedback.