Instructions: There are 6 pages and 10 multiple choice questions worth 5 marks each (zero for
more than one or for an incorrect answer, and +0.5 for no answer). Please make sure to record your
answers
University of Toronto
APM236 H1S: Applications of linear programming
2017 Course outline
Welcome to APM236! The main objectives of this course are to train you to:
produce and critically analyze math
APM 236

Linear Algebra
The following is a list of necessary linear Algebra for APM236. All these review material can be found in
your linear Algebra textbook as well as chapter zero of your linear P
APM 236H1F term test 2
9 November, 2011
FAMILY NAME
GIVEN NAME(S)
, STUDENT NUMBER
SIGNATURE
Instructions: N0 calculators or other aids allowed.
This test has 3 questions Whose values are gi
APM236
Practice Problems #3
October 17 21, 2016
1. Here are some extra practice problems for you in the aftermath of test 1.
(a) Consider the LPP of optimizing c> x over the polyhedron P = cfw_x Rn :
APM236
Practice Problems #1
September 19 23, 2016
1. Convert all of the following problems to standard form using matrix notation.
(a) maximize
x + 2y
subject to
3x + 4y 12
(d) minimize
subject to
x,
APM236
Practice Problems #0 Review
September 12 16, 2016
1. Find all solutions to the following linear systems.
(a) x
+ y + 3z = 5
3x 2y + 5z + u = 1
(b)
2x y + 4z = 11
x + y 3z + 2u = 2
y+ z =3
(c)
(
APM236
Tutorial #2 Convex costs
September 28 30, 2016
1. The function f : R R is defined by the following graph:
6
5
4
3
2
1
1
2
3
4
5
6
(a) Express f (x) as a maximum of three functions.
(b) Let A be
APM236
Practice Problems #4
October 24 28, 2016
1. B&T exercises 2.4, 2.10, 2.13, 2.14, 2.16, 3.1, 3.2, 3.3, 3.5.
2. In the proof of Theorem 2.7, we set things up so that x = y + (1 )z for some [0, 1]
APM236 study checklist
Disclaimer: This is not a list of things that will be on your test. It is just a handy guideline
to help you gauge what sorts of things you might be able to do to study more eff
APM236
Tutorial #1 Standard form
September 21 23, 2016
1. Write the following linear programs in standard form.
(a) minimize
subject to
(b) maximize
subject to
x y 7z
y+z 1
z9
(c) maximize
subject to
APM236
Tutorial #3 Extreme points & convex combinations
October 12 14, 2016
1. Find the extreme points of the sets below, and decide which ones are polyhedra. Which
of these sets has the property that
APM 236H1F term test 1 announcement, 3 October, 2012
1. No calculators are allowed.
2. The test will have 3 questions of approximately equal weight. Total marks = 40.
3. The test will cover Kolman and
MATH 103A Homework 8
Due March 15, 2013
Version March 20, 2013
Assigned reading: Chapters 9, 10 of Gallian.
Recommended practice questions:
Chapter 9 of Gallian, exercises
3, 4, 9, 11, 14, 15, 25, 37,
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Problem Sets
Page numbers below refer to Kolman and Beck, 2nd edition. It is recommended that you also do the odd
numbered problems, whose answers appear near the end of the book.
problem set 1: pg. 2
NAME: (Last, First)
duration 50 min., no aid allowed
Instructions: There are 5 pages and 10 multiple choice questions worth 5 marks each (zero for
more than one or for an incorrect answer, and +0.5 fo
APM 236

Linear Algebra
The following is a list of necessary linear Algebra for APM236. All these review material can be found
in your linear Algebra textbook as well as chapter zero of your linear P