Here is the blue/yellow test. Here is the the answer key. Here is the white/green test. Here is the answer key.

The midterm grades are ready. Please excuse my slowness in getting them done. You can pick up your exam in class or at my office hours. If you are very curious, send me email. The class average was 22. The grade distribution is: 0-9 = F, 10-13 = D, 14-16 = C-, 17-18 = C, 19-20 = C+, 21-23 = B-, 24-26 = B, 27-28 = B+, 29-30 = A-, 31-33 = A, 34-35 = A+. In terms of percentages: A's = 21%, B's = 39%, C's = 28%, D's = 6%, F's = 6%.

Here is how to find your "mark" on the first midterm. First you have to compute two numbers. For the first number, take the points you got on the exam and multiply it by 1.5102. Now add 37.8107. For the second number, take the points you got on the exam and multiply by 100/35. Your mark is the maximum of these two numbers. For example, if you got 12 points then your mark is 55.9 (the maximum of 55.9 and 34.3). There is one exception to this rule: if you got 14 points then your mark is 60.

Here is the diary of what I did in class. It includes information on how to start phase 2 once you've finished phase 1. In class, I just said "do Gaussian elimination and you'll get... Here're the details.

Here is the the yellow test. Here is the answer key.

Also, the full answer to #6b is as follows:

For the incoming variable x1, the candidates for exiting variables are x3, x2, x5, and x8. x2 and x8 are excluded because they'll never exit as you increase x1 (since the coeffecients in the matrix aren't positive). x3 is excluded because by the time it exits, x5 will have already exited. (The theta ratio for x3 is 2, while it's 1 for x5.) So the only possible exiting variable is x5.

For the incoming variable x4, the candidates for exiting variables are x3, x2, x5, and x8. x3 and x5 are excluded because they'll never exit as you increase x4 (since the coeffecients in the matrix aren't positive). x2 and x8 have equal theta ratios (they're both zero) so they're both legitimate choices for exiting variables.

For the incoming variable x6, the candidates for exiting variables are x3, x2, x5, and x8. x2 and x8 are excluded because they'll never exit as you increase x6 (since the coeffecients in the matrix aren't positive). x3 and x5 have equal theta ratios (they're both 1/3) so they're both legitimate choices for exiting variables.

For the incoming variable x7, the candidates for exiting variables are x3, x2, x5, and x8. x3, x2, and x5 are excluded because they'll never exit as you increase x7 (since the coeffecients in the matrix aren't positive). x8 is the only one left and is a legitimate choice for an exiting variable.

Here is the white test. Here is the answer key. Please see above for what a full answer to 6b would look like.

The second midterm is graded. You can pick up your exam in class or at my office hours. If you are very curious, send me email. The class average was 36. The grade distribution is: 0-9 = F, 10-19 = D, 20-24 = C-, 25-29 = C, 30-33 = C+, 34-36 = B-, 37-38 = B, 39-40 = B+, 41-43 = A-, 44-46 = A, 47-48 = A+. In terms of percentages: A's = 23%, B's = 42%, C's = 33%, D's = 2%, F's = 0%.

Here is how to find your "mark" on the second midterm. First you have to compute two numbers. For the first number, take the points you got on the exam and multiply it by 1.1024. Now add 35.0602. For the second number, take the points you got on the exam and multiply by 100/48. Your mark is the maximum of these two numbers. For example, if you got 39 points then your mark is 81.3 (the maximum of 78.1 and 81.3). There is one exception to this rule: if you got 21 points then your mark is 60.

We finished section 3.3 on March 13. On March 27, we will start section 5.1 and will spend the last three lectures (3/27, 4/3, and 4/10) covering sections 5.1-5.2, as well as discussing additional aspects of transportation and assignment problems.

If you look only at the course marks of the students who showed up to the final, the average course mark is 71. If you include the five students who didn't show up to the exam but were registered for the course, the average course mark is 69. A's: 17%, B's: 32%, C's: 41%, D's: 3%, F's: 8%.

If you are curious to find out your exam grade and your course mark, send me email.

Here is the final exam. Here is the answer key. NOTE: there are some mistakes in the answer to problem #2. Specifically, on page 7, the objective function should be "1/2 x2 - 7". The objective row of the tableau with basic variables x3, x1, and x5 should be "0 -1/2 0 0 0 -7". On page 8, the objective row of the tableau with basic variables x2, x1, and x5 should be "0 0 1 -1 0 -6". The objective function can still go to infinity --- there is on optimal solution.