HW6 - iterations If yes give the optimal solution Justify your answer Each question is independent 1(1 The RHS of the first constraint is changed

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
IEOR 262A Mathematical Programming I Fall 2007 Homework 6 (Due Friday, Nov 2, Before Discussion) Solve Exercise 4.2, 4.4 and 4.8 in the text book Introduction to linear optimization by Bertsimas and Tsitsiklis. Problem 1. Write the duals of following problems Verify that the dual of the dual is the original problem. (1) max 4 x 1 - 3 x 2 + 8 x 3 s.t. - 2 x 1 6 4 x 2 14 - 12 x 3 ≤ - 8 (2) max n j =1 c 0 j x j s.t. n j =1 a 1 j x j = b 1 n j =1 a 2 j x j b 2 n j =1 a 3 j x j b 3 x j 0 for all j (3) min 3 x 1 - 7 x 2 +6 x 4 +5 x 5 - x 6 s.t. 5 x 1 +8 x 2 +3 x 3 +3 x 4 +2 x 5 +11 x 6 = 200 Problem 2. Suppose we solve the following LP by simplex method. min 3 x 1 +2 x 2 - 3 x 3 - 6 x 4 +10 x 5 - 5 x 6 s.t. x 1 +2 x 2 + x 4 - 6 x 6 = 11 x 2 + x 3 +3 x 4 - 2 x 5 - x 6 = 6 x 1 +2 x 2 + x 3 +3 x 4 - x 5 - 5 x 6 = 13 x 1 x 2 x 3 x 4 x 5 x 6 0 We get the optimal basis B = { 1 , 2 , 3 } and B - 1 = - 1 - 2 2 1 1 - 1 - 1 0 1 . For each of the following changes in the LP, can you get the optimal solution to the new problem without any further
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: iterations? If yes, give the optimal solution. Justify your answer. Each question is independent. 1 (1) The RHS of the first constraint is changed from 11 to 13. (2) The coefficient of x 1 in the objective function is changed from 3 to-1, and the coefficient of x 4 in the objective function is changed from-6 to-4. (3) A new variable x 7 is added with cost coefficient-7 and the corresponding column vector A 7 = (1 , 2 ,-3) (4) The coefficient of x 5 in the second constraint is changed from-2 to-1. (5) A new constraint is added: x 1 + x 2-2 x 3 + x 4 ≥ 1. 2...
View Full Document

This note was uploaded on 09/16/2010 for the course IEOR 262A taught by Professor Don'trknow during the Fall '09 term at University of California, Berkeley.

Page1 / 2

HW6 - iterations If yes give the optimal solution Justify your answer Each question is independent 1(1 The RHS of the first constraint is changed

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online