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Unformatted text preview: x = 2 z , we have x = 2 X 1 6 ~ = 2 6 . At this point, we can con f rm the value of . From equation (7), = 2 x = 6 W = 0 . With the f rst constraint (2), the value of y can be found as y = x + z = X 2 6 ~ 1 6 = 2 6 1 6 = 3 6 . Now with ( x, y, z ) determined as ( x, y, z ) = X 2 6 , 3 6 , 1 6 ~ , at the extrema, f = 3 x y 3 z = 3 X 2 6 ~ X 3 6 ~ 3 X 1 6 ~ = 6 3 3 6 = 12 6 = 2 6 From here, we may infer that the maximum for f ( x, y, z ), under the constraints (2) and (3) is 2 6 and the minimum is 2 6. 2...
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This note was uploaded on 09/07/2011 for the course MATH 39578 taught by Professor Penner during the Spring '09 term at USC.
 Spring '09
 Penner

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