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# Find the extremum of z = xy subject to x + y = 6 Watch

1. Please help with the following: Find the extremum of z = xy subject to x + y = 6

By substituting from the constraint into the objective function.
And by Lagrange's method..

Thanks
2. (Original post by JKITFC)
Please help with the following: Find the extremum of z = xy subject to x + y = 6

By substituting from the constraint into the objective function.
And by Lagrange's method..

Thanks
I suggest you learn about Lagrange multipliers before, since this is a basic application that comes from learning
3. Use the AM-GM inequality to find an upper bound for (xy)^0.5, hence xy
4. (Original post by 123Master321)
I suggest you learn about Lagrange multipliers before, since this is a basic application that comes from learning
I know it... I cant do the systems of equations that it produces
5. (Original post by JKITFC)
I know it... I cant do the systems of equations that it produces
Ok, so:

6. (Original post by MarcusRashford19)
Use the AM-GM inequality to find an upper bound for (xy)^0.5, hence xy
OP was asking for using Lagrange multipliers, otherwise you could just let y=6-x, put it into the other equation and differentiate, no need for AM-GM

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Updated: November 14, 2016
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