My Math Forum Fastest structured way to get max(abc) if a+b+c=30
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January 24th, 2019, 07:50 AM   #11
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Quote:
 Originally Posted by idontknow How to find the minimal value (a fast way)?
There isn't any. The method, Romsek-Lagrange multipliers, and mine-based on principle behind Lagrange multipliers, picks up all extrema.

EDIT:

Actually, the most basic way to look for extrema is to substitute for z to get:
H(x,y)=xy(30-x-y)
Then Hx=Hy=0 gives x=y=z=10.

Last edited by zylo; January 24th, 2019 at 08:23 AM.

January 24th, 2019, 08:23 AM   #12
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Quote:
 Originally Posted by zylo There isn't any. The method, Romsek-Lagrange multipliers, and mine-based on principle behind Lagrange multipliers, picks up all extrema.
you can apply the 2nd derivative test to the solutions found and weed out non-maxima

The harder problem is if the maxima is on the boundary in which case it won't be picked up using Lagrange Multipliers at all.
As far as I know in that case you just have to check the boundaries using brute force.

 January 24th, 2019, 08:29 AM #13 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 There is only one solution. What boundary? There isn't any. If you accept 0's, the minimum of xyz is x=0, y=0, z=30 EDIT Again: With that in mind, recalling v8archie's suggestion, the nearest integers would be x=1, y=1, then z=28. Looks reasonable but can't prove it. Last edited by skipjack; January 24th, 2019 at 11:48 AM.

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