Assignment 2
Due: Wednesday October 10 at the BEGINNING of class
1. Convert the following linear programs into standard equality form:
(a)
minimize
subject to
2x1 + 3x2 + 4x3
8x1 + x3 2
3x2 8x3 1
x1 0
Solution: maximize
subject to
(b)
maximize
subject to
Assignment 5
Due: Wednesday November 30 at the BEGINNING of class
1. Write down any 3 Chvatal-Gomory cuts for EACH linear program. Explain how you
derive each one.
(a)
maximize
subject to
2x1 + x2 x3 + 3x4 + x5
9
11
4
x1 + x2 + x4 + x5
3
7
5
6
8
3x1 + x2
Assignment 3
Due: Wednesday October 26 at the BEGINNING of class
1. Given the following linear programs with feasible basis B, do the following:
(i) solve the linear program without tableau, give an appropriate certificate
(ii) solve the linear program wi
CO 227 Assignment 4
Due: Wednesday November 16 at the BEGINNING of class
1. Given the following linear programs, write down the corresponding dual linear program:
(a)
(b)
(c)
maximize
subject to
x1 2x2 + 3x3 4x4 + 5x5
7x1 + 9x3 + 2x4 x5
2x1 3x2 + x4 + 3x5
CO 227 - Assignment 1 - Fall 2016
Due: Wednesday September 28 at the BEGINNING of class
Note: Do NOT attempt to solve any of the mathematical programs you come up with for
this assignment.
1. Prof. Roh is selling copies of the latest Justin Bieber CD.
The
UNIVERSITY OF WATERLOO
MIDTERM EXAMINATION
FALL TERM 2011
Student Name (Print Legibly)
(family name)
(given name)
Signature
Student ID Number
COURSE NUMBER
CO 227
COURSE TITLE
Introduction to Optimization
COURSE SECTION
001
DATE OF EXAM
Wednesday, Novembe
Assignment 4
Due: Wednesday November 14 at the BEGINNING of class
1. Given the following linear programs, write down the corresponding dual linear program:
(a)
maximize
subject to
Solution:
(b)
maximize
subject to
Solution:
(c)
minimize
subject to
6x1 3x2
Assignment 3
Due: Wednesday October 24 at the BEGINNING of class
1. Given the following linear programs with feasible basis B , do the following:
(i) solve the linear program without tableau, give an appropriate certicate
(ii) solve the linear program wit
Assignment 3
Due: Wednesday October 24 at the BEGINNING of class
1. Given the following linear programs with feasible basis B , do the following:
(i) solve the linear program without tableau, give an appropriate certicate
(ii) solve the linear program wit
Assignment 2
Due: Wednesday October 10 at the BEGINNING of class
1. Convert the following linear programs into standard equality form:
(a)
minimize
subject to
2x1 + 3x2 + 4x3
8x1 + x3 2
3x2 8x3 1
x1 0
(b)
maximize
subject to
4x1 7x2 + x3
5x1 3x2 + x3
x1 +
Assignment 1
Due: Wednesday September 26 at the BEGINNING of class
1. Pats Porsches is a local company that makes cars that look like Porsches.
There are 2 suppliers (S1,S2) that provide the steel to make the cars. Each supplier
can supply the following a
Assignment 1
Due: Wednesday September 26 at the BEGINNING of class
1. Pats Porsches is a local company that makes cars that look like Porsches.
There are 2 suppliers (S1,S2) that provide the steel to make the cars. Each supplier
can supply the following a