Acknowledgements

I would like to thank Professor Paul Kergin, for providing me with with a lot of his course materials from his many years of experience teaching this course in the past.

Final Exam Office Hrs

Please note that all regular office hours have ended, and these are the office hours for the final week of the semester.

Tuesday 3-5 pm RM. HU 1018 Rosemonde
Wednesday 12-2 pm RM. HU 1018 Elio
Thursday 1-3 pm RM. HU 1018 Elio
Thursday 3-5 pm RM. HU 1018 Rosemonde

APM 236H1F Announcements

  • The final problem set #7 of the year is short and is practice forming the dual problem. See below.

  • The final exam info is available here.

  • Problem set 6 has been posted below. It is practice with the simplex method.

  • The solutions to Quiz 3 have been posted below.

  • The extra office hours for Quiz#3 will take place in HU 1018 from 1.10-3 pm on Thursday with me (Elio).

  • The solutions to the questions from Problem set 5 (that don't have solutions) is available here

  • I have posted the Quiz3 info below.

  • We won't be using the KB textbook any longer. It has served its purpose. Read more about it here

  • Problem set 5 has been posted below. It is practice with basic directions and reduced cost.

  • The solutions to Quiz 2 have been posted below.

  • Correction to a remark made below for PS4, Q#7, pg 100. (see below).

  • This week, the week of the Quiz #2, our TA will hold extra office hours. These will take place on Thursday 3-5 pm in the SS Math Aid Centre (MAC). Her regular office hours in SS 2111 will also continue to take place on Monday 1-2 pm, Wednesday 5-6 pm.

  • The instructor will also hold office hours on Wednesday before class from 11-12, outside of our lecture room MP 102.

  • Please check to make sure that your grade for Quiz #1 on portal corresponds to the grade on your paper. The deadline for any corrections to your grade is this Wednesday, October 21st, 2015.

  • This week, the week of the Quiz #1, our TA will hold extra office hours. These will take place on Thursday 3-5 pm in the SS Math Aid Centre (MAC). Her regular office hours in SS 2111 will also continue to take place on Monday 1-2 pm, Wednesday 5-6 pm.

  • The instructor's office hour tomorrow (Wednesday, Oct 7th) will take place before class from 11-12 in SS 2112.

    • Quiz information

    Read here for quiz 3 info Here are the solutions.

    Read here for quiz 2 info Here are the solutions.

    Read here for quiz 1 info. Here are the solutions.

    Links To Items Related To APM 236H1F

    The course outline.

    The U. of T. library's copy of Kolman and Beck. Here is a copy of page 42, which is missing from the library's copy.

    Notice:

    I have attached a short note on the terminology differences between our two textbooks. Please take a look at it here.

    TA Office Hrs:

    Our TA (Rosemonde) will have two office hrs each week. They will take place on Monday 1-2 pm Wednesday 5-6 pm in SS 2111. Please make use of them, if you can!

    Problems to work on:

    Apart from these problems, it is recommended that you also work on the odd-numbered problems from KB, which have answers at the back of the book.

    Problems 1. Read Chapter 0 of Kohlman and Beck to review your linear algebra background. Then, solve the following questions. Problem set 1: p 21, #6b. (Additional instructions: (i). Solve for x, y, and z in terms of w. (ii). Solve for x, z, and w in terms of y.) p 21, #9a, p 28, #6c, #8b, p 42, #5d, #6b.

    Problems 2. Read Section 1.1. of Kolman and Beck. Solve the following: pg. 57 #2, #4, pg. 58 #6, #8, pg. 59 #10. Put these problems in canonical form (standard "equality" form).

    Problems 3. You can find the problems here.

    problem set 4: p 82, #14. p 83, #16. In the preceding questions, replace instructions (b) and (c) with "draw the line z = c^T x = k, where k is the optimal value of z." p 91, #4, #8, #12. p 100, #6, #8. (NOTE: if you try doing problem #7 on page 100, you'll discover that the answer in the back of the book is wrong. The correct answer is: 7a: not a basic solution since it doesn't satisfy Ax=b. 7b: is *NOT* a basic solution because C2,C3,C5 are l-dependent*. 7c: is a basic solution with basic variables x1, x3, and x5. *BUT NOT* with x2, x3, and x5. *Also works* with x3, x4, and x5.)*Correction.

    Supplementary problems: 1. Prove that the set of optimal solutions of any linear programming problem is convex. 2. Prove that the set of objective values which a linear programming problem attains over its feasible region is convex. 3. Give an example of a convex set in R^2 which is not a line segment, and which has (1,0) and (0,2) as its only extreme points. 4. Find all extreme points (in R^3) of the set {(x1,x2,x3) such that x1 - x2 + x3 = -1, 3 x1 - 2 x2 + 4 x3 = 2, x1 + x2 + 3 x3 = 9, x1 >=0, x2 >= 0, x3 >= 0}.

    Problems 5. You can find the problems here.

    Problems 6. You can find the problems here.

    Problems 7. From the KB Textbook: Section 3.1, pg 166 #2,4,6.

    Solutions to problem sets: 1, 2 3 4 5

  • Problem set 6 came with solutions included.
  • Problem set 7 solutions can be found here.

    • Here is a link to portal.

    The Faculty of Arts and Science page on student academic integrity.