Math 340 Assignments

General remarks

  1. Homework should be legible and neat, questions should be answered in order, and pages should be fastened with a staple with your name and student number on at least the front page in pen.

  2. Homework will be collected on Thursdays in class and will cover the material through Tuesday's lecture (roughly). You should start attempting the problems as soon as possible after the material is presented in lecture. Please don't save it all for Wednesday night.

  3. Solutions should be written carefully, using good English, complete sentences, and adequate detail, with citations from the book or notes. Some of these solutions may be expanatory proofs. A good guideline here is that you should write proofs the way you would like to see them in your textbook. In summary,  show all your working to get full marks.

  4. Some of the textbook problems have hints in the back of the book. If you get stuck on a problem, you might find it helpful to look at a similar textbook problem that has a hint. These problems also make good practice problems.

Assignment 1, due Thursday January 12th

Covering Chapter 1: Standard form, geometric problems

1. Problem 1.2
2. Problem 1.3

Assignment 2, due Thursday January 19th

Covering Chapter 2: The revised graphical method

1. Problem 1.1(c) using the revised graphical method
2. Problem 2.1(c) using the revised graphical method

Assignment 3, due Thursday January 26th

Covering Chapter 2: The simplex method

1. Problem 2.1(b)
2. Problem 2.2

Assignment 4, due Thursday February 2nd

Covering Chapter 3: Three types of problem

1. Problem 3.9 Advice: This can take long.
2. Problem 3.10 Hint:  prove or disprove in each direction to get the answer.

Assignment 5, due Thursday February 16th

Covering Chapter 5: Duality

1. Solve the dual of 2.1(a)
2. Solve the dual of 2.1(b)

Assignment 6, due Thursday, March 1st

Covering Chapter 5: More duality and complementary slackness

1. Problem 5.2
2. Problem 5.3(a)

Assignment 7, due Thursday, March 8th

Covering Chapter 5: Economic interpretations

1. Problems 1.7, 5.5
2. Problem 5.8

Assignment 8, due Thursday, March 15th

Covering matrices

1. a) A k x k matrix W is called symmetric if the transpose of W is W. Prove that if A is any k x k matrix then A plus (A transpose) is symmetric.
b) A k x k matrix W is called skew-symmetric if the transpose of W is -W. Prove that if W is skew-symmetric then the entries on the main diagonal are 0.

2. If A and B are k x k matrices, prove that AB=BA if and only if (A+B)(A-B)= (A-B)(A+B).

Assignment 9, due Thursday, March 22nd

Covering Chapter 7: Revised simplex method

1. Problem 7.1 for 2.1(b)
2. Problem 7.5

Assignment 10, due Thursday, March 29th

Covering Chapter 7: Revised simplex method and efficiency

1. You have 40, 50, and 70 pounds of types A, B, and C of coffee. You have found three blends that sell well. One blend X consists of 1, 2, and 2 pounds of coffees A, B, and C, and gives you a profit of $3; one blend Y consists of 1 pound of each A and C with a profit of $2; and one blend Z consists of 2, 3, and 3 pounds of A, B and C with a profit of $4. Used the revised simplex method with eta factorisation and the smallest subscript rule to determine how much of each blend you should produce.
2. In terms of making things more efficient, what advantage does the smallest subscript rule have over the largest coefficient rule when using the revised simplex method?

Assignment 11, due Thursday, April 5th

Covering Chapter 10: Sensitivity analysis

Problems (a), (b), (c), (d), (e)

Back to course home page.