August 31st, 2013, 04:06 AM  #1 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 878 Thanks: 60 Math Focus: सामान्य गणित  minimum value of function
minimum value of when subjected to and satisfies the condition. but I'm not able to show all three at a time I want someone to explain me the problem. 
August 31st, 2013, 05:46 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,193 Thanks: 504 Math Focus: Calculus/ODEs  Re: minimum value of function
Because of the cyclic symmetry of the variables, the minimum is found when: You will easily find this is true using Lagrange multipliers. 
August 31st, 2013, 08:11 AM  #3 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 878 Thanks: 60 Math Focus: सामान्य गणित  Re: minimum value of function
I can see , and has similar role, nothing happens if we interchange their position. could u please explain me in simple words. 
August 31st, 2013, 08:46 AM  #4  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: minimum value of function Quote:
In any case, what have you tried?  
August 31st, 2013, 09:42 AM  #5 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 878 Thanks: 60 Math Focus: सामान्य गणित  Re: minimum value of function
what I did is, f = x + y + z . . . . (i) x + y + z  1 = 0 . . . . (ii) xyz + 1 = 0 . . . . (iii) we know, x + y + z = ( x + y + z)  2xy  2yz  2xz f = 1  2xy  2yz  2xz substituting value of "z" from equation (iii) f = 1  2xy + 2/x + 2/y . . . . (vi) partially differentiating equation (vi) w.r.t x and y and equation the results with zero, yx =  1 . . . . (v) xy =  1 . . . . (vi) combining (v) and (vi) yx  xy = 0 xy ( x  y ) = 0 thus, x = y why am i getting x = y if x = y, I get only (1, 1, 1) and don't get other point. is the process I followed incorrect ? 
August 31st, 2013, 09:47 AM  #6 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 878 Thanks: 60 Math Focus: सामान्य गणित  Re: minimum value of function
[color=#800040]Mark[/color] there are two conditions, x + y + z  1 = 0 and xyz + 1 = 0 I don't know latex properly, so may b second condition is not displayed properly. 
August 31st, 2013, 10:08 AM  #7  
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,193 Thanks: 504 Math Focus: Calculus/ODEs  Re: minimum value of function Quote:
For which we find the real solutions: and:  
August 31st, 2013, 10:21 AM  #8 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 878 Thanks: 60 Math Focus: सामान्य गणित  Re: minimum value of function
Could u please tell me someone about first three equations. also, mew and lamda. 
August 31st, 2013, 10:27 AM  #9 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,193 Thanks: 504 Math Focus: Calculus/ODEs  Re: minimum value of function
I assumed that if you are studying optimization with constraints, then you are familiar with Lagrange multipliers. I simply do not have the patience with the quirky rendering of here to attempt a tutorial on the subject.

August 31st, 2013, 10:33 AM  #10 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 878 Thanks: 60 Math Focus: सामान्य गणित  Re: minimum value of function
:'(


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