IND ENG 160 Study Guide - Midterm Guide: Industrial Engineering, And1, Lagrange Multiplier

• School: Berkeley
• Department: Industrial Engineering And Operations Research
• Course: IND ENG 160
• Professor: All

Document Summary

The k-t conditions yield min f (x) = (x a)2 s. t. x b x c. If x = b, 2 = 0, 1 = 2(x a) = 2(b a) If x = c, 1 = 0, 2 = 2(x a) = 2(c a) Here we begin to discuss in cases: a < b, holds, 2 > 0, contradictory to (2, x = a, contradictory to b < x < c. So x = b, 1 = 2(b a), 2 = 0, f (x ) = (b a)2: b < a < c, 1 < 0, contradictory to (1) ii) 2 > 0, contradictory to (2) iii)holds. So x = a, 1 = 2 = 0, f (x ) = 0: c < a, 1 < 0, contradictory to (1, holds, x = a, contradictory to b < x < c. So x = c, 1 = 0, 2 = 2(c a), f (x ) = (c a)2.