(b) (Challenge Problem) Show that if x1 + x2 + ·… +¤n = 1, and each r; > 0, then п — 1 2n 1

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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Need help with part b). Please explain each step and neatly type up. Thank you :)

 

4. (a) Use the method of Lagrange multipliers to show that if x1+x2+x3 = 1l and r1, x2, x3 > 0,
then
1
T1T2+ I113 +1213
(b) (Challenge Problem) Show that if x1 + x2 + · · ·+ ¤n
= 1, and each r; 2 0, then
n – 1
2 Titj <
2n
1<i<j<n
Transcribed Image Text:4. (a) Use the method of Lagrange multipliers to show that if x1+x2+x3 = 1l and r1, x2, x3 > 0, then 1 T1T2+ I113 +1213 (b) (Challenge Problem) Show that if x1 + x2 + · · ·+ ¤n = 1, and each r; 2 0, then n – 1 2 Titj < 2n 1<i<j<n
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