Use Lagrange multipliers to find three positive numbers whose sum is 100 and whose product is maximum.
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Find three positive numbers whose sum is 100 and whose product is a maximum.
Solution: Let the three numbers be x, y and z. ...
y = 100 / 3. Let A = xx = -2x, B = xy = 100 - 2x -2y, C = yy = -2y. ...
z = 100/3. ∴ Maximum product is at (100/3, 100/3, 100/3). ...
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