I'm a bit confused on how to approach this question. Suppose the
number of cars per hour given in the Table below can
travel between any two of the towns A, B, C, & D. Determine how many
cars can be sent from Town A at 12pm to Town D at 3pm.

From Town A 
to Town A: - -
to Town B: 200
to Town C: 150
to Town D: 250

From Town B
To Town A: 200
To Town B: - -
To Town C: 220
To Town D: 230

From Town C
To Town A: 150
To Town B: 220
To Town C: - -
To Town D: 180

From Town D
To Town A: 250
To Town B: 230
To Town C: 180
To Town D: - -

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Clarification of Question by eiffeltower-ga on 17 Nov 2005 07:10 PST

There has to be a list of decision variables and constraints in this
modeling question.

no timings in question e.g timings of departure or arrival at differents stations?

is it 6oo, there are three routes from A to D.
1) A to D directly. 250 buses
2)A-B-D 200 buses
3)A-C-D 150 buses
 total 600 buses

We need to clarify the question.  Based on what you wrote we can assume that 
(1) each town is an hour away from every other town
(2) cars leave once an hour to go to another town at 12PM, 1PM and 2PM
and arrive at 1PM, 2PM and 3PM
(3) the entire transportation network is at the disposal of maximizing
the number of cars that travel directly or indirectly from town A to
town D

For direct travel, at 12PM, 1PM and 2PM, 250 cars an hour leave Town A
for Town D, arriving at 1PM, 2PM and 3PM, for a total of 750 cars.

For indirect travel, we note that 200 cars an hour can leave town A
for town B and 150 cars an hour can leave town A for town C.  This
creates no bottlenecks, since 230 cars an hour can travel from town B
to D and 180 cars an hour can travel from town C to D.  So all the
cars leaving town A for towns B and C can arrive in town D two hours
later.

So we note that 200 + 150 = 350 cars an hour leave town A for towns B
and C at 12PM and 1PM, leave those towns at 1PM and 2PM, and arrive in
town D at 2PM and 3PM for a total of 700 cars.

So in total 750 + 700 or 1450 cars can leave town A and arrive in town
D in the time alloted.