Find all the points (x, y, z) with x, y, z => 0 which maximizes the function
f(x, y, z) = xy + xz + yz - 4xyz subject to the constraint x + y + z = 1.
Please do NOT "hijack" other peoples threads by asking completely unrelated questions in them! It is extremely rude.
guess, use the "Lagrange Multiplier Method"- the max or min of f(x,y,z) subject to the constraint g(x,y,z)= constant must satisfy for some number .
For this problem, that is . That is, you have , and .
Those fairly easily reduce to y+ z- 4yz= x+ z- 4xz and y+ z- 4yz= x+ y- 4xy. Together with x+ y+ z= 1, you have three equations to solve for x, y, and z.
well , i am not keen on inequalities but i think it is a great attempt !
the equality holds when
but it may be wrong because we can find that :
I hope it will be perfectly corrected by some experts .