Comments on Assignment 3
Q#14 was in general fairly well done. Below are just some common problems:

- some students forgot to put in an extra arc (of zero flow) to the degenerate initial basic feasible solution to make it a spanning tree.
- a lot of students used notations that they did not define or explain. Many did not follow the format given in the course outline.
- once one of the dual variables is chosen arbitrarily, the others should be calculated using the formula of zero reduced costs.
- most students failed to economically interpret the dual variables

Brief marking scheme:
part (a): 3
part (b): 3
part (c): 5 (Note: students are not required to generate two extra initial bfs and hence not required to compare their "closeness" to optimality)
part (d): 3
part (e): 3
overall presentation/format: 3

Q#17 was in general poorly done.

- the values of the dual variables given in the question are incorrect. This might have caused some confusion, though the errors should not directly affect the solutions.
- the biggest problem lies in part (d), where almost no students got all the correct answers. I approach the problem by adding a new node to the original graph to take care of the supply/demand shortage/surplus, and then I calculate the amount of surplus or shortage necessary to alter the spanning tree that corresponds to the original optimal solution. Very few students followed this approach

Brief marking scheme:
part (a): 4
part (b): 4
part (c): 2
part (d): 8
part (e): 2

Consistent with the previous assignments, the other two questions were not marked. 10 marks are awarded to each whenever the question seems to be reasonably attempted.