Let M = M₁U M₂ UM3 and K M₁ = {(x1, x2) ER²: 2 ≤ x ≤ 8, 2≤ x ≤8}, M₂ = {(x1, x2)™ € R² : 4 ≤ x₁ ≤ 6, 0 ≤ x2 ≤ 10}, M3 = {(x1, x2) Є R²: 0 ≤ x₁ ≤ 10, 4≤ x ≤ 6}, ¯ = cone {(1, 2), (1,3)†} ≤ R². (a) Determine the set E(M,K) of efficient points of M with respect to K. (b) Determine the set P(M, K) of properly efficient points of M with respect to K.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 18E
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Let
M = M₁U M₂ UM3 and K
M₁ = {(x1, x2) ER²: 2 ≤ x ≤ 8, 2≤ x ≤8},
M₂ = {(x1, x2)™ € R² : 4 ≤ x₁ ≤ 6, 0 ≤ x2 ≤ 10},
M3 = {(x1, x2) Є R²: 0 ≤ x₁ ≤ 10, 4≤ x ≤ 6},
¯ = cone {(1, 2), (1,3)†} ≤ R².
(a) Determine the set E(M,K) of efficient points of M with respect to K.
(b) Determine the set P(M, K) of properly efficient points of M with respect to K.
Transcribed Image Text:Let M = M₁U M₂ UM3 and K M₁ = {(x1, x2) ER²: 2 ≤ x ≤ 8, 2≤ x ≤8}, M₂ = {(x1, x2)™ € R² : 4 ≤ x₁ ≤ 6, 0 ≤ x2 ≤ 10}, M3 = {(x1, x2) Є R²: 0 ≤ x₁ ≤ 10, 4≤ x ≤ 6}, ¯ = cone {(1, 2), (1,3)†} ≤ R². (a) Determine the set E(M,K) of efficient points of M with respect to K. (b) Determine the set P(M, K) of properly efficient points of M with respect to K.
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