I have a software problem and I'm searching for a solution but tried
different algorithm approach and nothing came out.
I'm not very familiar with all the graph algorithms and I hope there
is already a way to solve this kind of problems in polynomial time.

I need the algorithm for different task but I illustrated simple like
this:

The are N cities and there is a wanderer.
The time it takes for him to go from a town to another town is known -
Txy (from town x to town y).
>From any town he can go to another town so it is a complete graph.
In each town there is a an amount of money Mx the wanderer wants to
collect.
It isn't enough time to pass through all cities.
Having the total available time T and the starting point i, the
problem is to find the best route so that the money he collects will
be maximum.

Input numbers range:
N is between 400 and 600
Mx(M1, M2, ...) are between 50 and 500, x between 1 and N
Txy are between 1 and 200, x and y are between 1 and N, x!=y
T is between 1000 and 5000


The problems is shared here:
http://www.evernote.com/shard/s119/sh/79f47a65-c1e6-44da-bbc0-7d10e36c7f71/374eda2f355c9a18d41ea19a20866fbc

Thanks

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