Decision 2

Dynamic programming is usually worth quite a lot of marks (sometimes up to about 13 or 14), and can easily catch people out if they throw in a tricky table-form question. But, as you've said, travelling salesman and allocation aren't usually worth too many.

For game theory, if you're comfortable with setting-up the three equations for V(A) in terms of p when determining a player's best strategy, you should be fine. The graph is really easy to sketch after that; the optimal point of intersection part is somewhat trickier, though. Just look for the highest point of intersection where the other line passes vertically above this point (rather than below it). I really can't imagine them asking another question on formulation of game theory as a linear programming problem - they've done that for like the last two years! (It wouldn't hurt to still know it, though!) Make sure that you can deduce stable/unstable solutions from row maximin and column minimax (this way around) - for sometimes up to 3 marks - and know how to reduce a pay-off matrix, too. Also, remember that, for a zero-sum game, V(A)+V(B) = 0.

The north-west corner method is easy enough; remember to always set the first row's shadow cost equal to zero, and only use the costs of "routes" currently being used to calculate the rest. Remember to calculate ALL possible improvement indices for alternative cells; also, even if one is the smallest, it should only be used if it is negative (otherwise the solution is optimal). Enter theta into the entering cell (remember to state your entering cell clearly - that's usually a mark!), and then just gradually fill-out the rest of the cells in an order which definitely works. Anything in its own row and/or column in the initial solution, which is also not in line with the new entering cell, must stay the same (as only one new entering cell can be added at a time). Also, NEVER put a zero in a cell unless the solution would otherwise be degenerate (just leave it blank).