Math 340 Exams

Midterm, Tuesday 7th February, 11.00-12.30, Location  SCRF 100


The midterm will cover chapters  1-4. (Homeworks  1-4.) It is a closed-book exam: no books, notes, or calculators may be used.

The goals and topics covered are:  changing word problems to LP problems, writing problems in standard form, finding feasible solutions geometrically, distinguishing 3 types of LP problem, proving unbounded using a possible maximum M, using the graphical method, using the revised graphical method, applying the simplex method, finding all optimal solutions, initialization: creating and solving the auxiliary problem, applying the two-phase simplex method, identifying infeasible/unbounded LP problems with the simplex method, iteration: finding entering and leaving variables, termination: understanding the roles of cycling and degeneracy, recalling and applying pivoting rules.

Extra office hours:   Monday 6th February 5-6pm

Practice questions:  Here are two small practice quizzes from previous years (with solutions) quiz 1, quiz 2 (Anstee's rule is the largest coefficient rule).

Some study hints:

  1. This is a Math Majors course, which means the exam will be about 50% proofs 50% calculation. You will be expected to prove results like on the homework, or in class.
  2. To study efficiently make sure you know the definitions, the algorithms/methods for computing things, the formulas for things, and results/proof methods we use most often. Perhaps write them in your own words, or explain them to a friend.
  3. Do the lecture examples, practice questions and old homeworks again without looking at the answers.
  4. Got through the posted homework solutions to gain another point of view on solving the questions.
  5. In the exam: If you get stuck on a problem in the exam then write down relevant definitions accurately. This will help to inspire you and pick up points for working. If you use a result from class say "From the result in class..." then state the result so the grader knows this isn't made up.

Final exam, Thursday 12th April, 3.30-6.00 pm, Location GEOG 100

The final will cover the whole course, which is chapters 1-7, 10. (Homeworks 1-11.) It is a closed-book exam: no books, notes, or calculators may be used.

The goals and topics covered are:  changing word problems to LP problems, writing problems in standard form, finding feasible solutions geometrically, distinguishing 3 types of LP problem, proving unbounded using a possible maximum M, using the graphical method, using the revised graphical method, applying the simplex method, finding all optimal solutions, initialization: creating and solving the auxiliary problem, applying the two-phase simplex method, identifying infeasible/unbounded LP problems with the simplex method, iteration: finding entering and leaving variables, termination: understanding the roles of cycling and degeneracy, recalling and applying pivoting rules.

Recalling the fundamental theorem of linear programming, stating and applying the weak and strong duality theorems, determining unbounded/infeasible problems with duality, applying complementary slackness, deriving economic interpretations, deriving the linear algebra of LP problems, applying the revised simplex method, deduding the dual solution with the revised simplex method, implementing eta factorization, implementing sensitivity analysis: changing the objective function, changing the resources, the dual simplex method, dual pivoting, adding a variable, adding a constraint.

Office hours: Tuesday 10th April 3-5pm

Practice questions: Here is a past final with very brief solutions to practice with (you can't do questions 4(b), 4(c), 6). Also Problems (f), (g).

Some study hints:

  1. This is a Math Majors course, which means the exam will be about 50% proofs 50% calculation. You will be expected to prove results like on the homework, or in class.
  2. To study efficiently make sure you know the definitions, the algorithms/methods for computing things, the formulas for things, and results/proof methods we use most often. Perhaps write them in your own words, or explain them to a friend.
  3. Do the lecture examples, practice questions and old homeworks again without looking at the answers.
  4. Got through the posted homework solutions to gain another point of view on solving the questions.
  5. In the exam: If you get stuck on a problem in the exam then write down relevant definitions accurately. This will help to inspire you and pick up points for working. If you use a result from class say "From the result in class..." then state the result so the grader knows this isn't made up.

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