This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 μ . From equation (7), μ = 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...
View
Full Document
 Spring '09
 Penner
 Optimization, Southern California, Class Problem, ﬁrst constraint, extremum values

Click to edit the document details