Finding the conditional extremum of the function z = XY satisfying the condition x + y = 1

X + y = 1. = = = > y = 1-x. = = > z = xy = x (1-x) = - x ^ 2 + X. = = > z = - x ^ 2 + x = - [x - (1 / 2)] ^ 2 + (1 / 4). = = = > when x = y = 1 / 2, Zmax = 1 / 4

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