C&O 350 Linear Optimization Fall 2009 Solutions to Assignment 1
Question # 1 2 3 4 5 Total 1. (Linear Algebra Review) 6 marks = [2+2+2] Solution: (a) S is a linearly independent set if and only if for all scalars c1 , . . . , cn , the equation implies tha
Assignment 6 Solutions
1. (a) Show that if there is a tie for the choice of leaving variable in an iteration of the simplex
method, then the new basis is degenerate. Deduce that there is never a tie for the choice
of leaving varia
Due: July 9 at 2pm.
Your full name, student ID number, the course number, and the name of your instructor should all be
clearly visible on the front of your assignment.
Exercise 1: For the following pairs (A, b) solve the feasibility pr
C O350 L INEAR P ROGRAMMING - A SSIGNMENT 5
Due Date: Friday June 18 at 2 PM in assignment drop box 2, in front of MC4066.
Please make sure that your name and student number, the course number, and the name of your instructor
are clearly written on the fr
CO350/CM340/CO352 Linear Optimization - Fall 2006
Midterm Solutions Problem 1: Basic Solutions (a) (i) No. (ii) Yes. (iii) No. (b) We have 02 20 x3 x4 = 8 4 .
Now 2x4 = 8 implies x4 = 4, and 2x3 = 4 implies x3 = 2. So the corresponding basic solution is [
UNIVERSITY OF WATERLOO MIDTERM EXAMINATION SUMMER TERM 2007
Surname: First Name: Signature: Id.#: Section#: Course Number Course Title Instructors Date of Exam Time Period Exam Type Additional Materials Allowed CO350 Linear Optimization J. Geelen, B. Guen
C&O 350 Linear Optimization Fall 2009 Solutions to Assignment 2
Question # 1 2 3 4 5 6 (Bonus) Total 1. 6 marks = [3+3] Solution: (a) To convert the given LP to standard inequality form, we can do the following: (i) Substitute x3 by u3 v3 , where u3 , v3
C O350 L INEAR P ROGRAMMING - S OLUTIONS TO ASSIGNMENT 8
Exercise 1. Consider the linear program
(P ) maxcfw_cT x : Ax = b, x 0
where A Rmn , c Rn and b Rm . Let B be an optimal basis for (P ), let x be the associated basic
solution, let R and let d be th