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We are looking for a solution of this function : f ∶ R2 → R (x, y) → x2+ y2− 4x + 4 with constraint  :  min f(x,y) / (x,y) in K2 --> K2={(x,y) in R2 ; 2x-y2 <= 1 & x >= 0}   a) show that if (x',y') is a local minimum : (x',y') in {(1,-1),(1,1),(0.5,0)} b) calculate f(1, 1), f(1, −1) and f(0.5, 0).

We are looking for a solution of this function : f ∶ R2 → R (x, y) → x2+ y2− 4x + 4 with constraint  :  min f(x,y) / (x,y) in K2 --> K2={(x,y) in R2 ; 2x-y2 <= 1 & x >= 0}   a) show that if (x',y') is a local minimum : (x',y') in {(1,-1),(1,1),(0.5,0)} b) calculate f(1, 1), f(1, −1) and f(0.5, 0).

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 35CR: Maximize the function fx,y=7x+5y in the region determined by the constraints of Problem 34.
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We are looking for a solution of this function :

f ∶ R2 → R
(x, y) → x2+ y2− 4x + 4

with constraint  : 

min f(x,y) / (x,y) in K2 --> K2={(x,y) in R2 ; 2x-y2 <= 1 & x >= 0}

 

a) show that if (x',y') is a local minimum :

(x',y') in {(1,-1),(1,1),(0.5,0)}

b) calculate f(1, 1), f(1, −1) and f(0.5, 0).

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