Networking?

[Timinator]

My problem in a nutshell:

I own a truck company.

I must visit 3 cities to show off my trucks to customers.

There are a total of 6 cities in the township and I start from city 1.

There are bridges between each city and each hold a maximum weight (thus limiting the weight of my truck)

The info I have is as follows

6 cities in total
city 3,4,6 must be visited
you may enter and exit a city as many times as you want.

bridges are as follows

between city 1 and 2 the maximum bridge capacity is 60

between city 1 and 6 the maxium bridge capacity is 20

between city 1 and 4 the maximum bridge capacity is 30

between city 4 and 5 the maximum bridge capacity is 90

between city 5 and 6 the maximum bridge capacity is 40

between city 2 and 3 the maximum bridge capacity is 10

between city 4 and 3 the maximum bridge capacity is 50

What I need

The maximum weight I can take to go to all three of the needed cities.

Example

since I start from city 1 I can go to city 4 (weight = 30) then city 3 (weight = 50)then back to city 4 (weight = 50) then city 5 (weight = 90) then city 6(weight = 40)

Any other way will give a lower value

Therefore the maximum weight I can take is 30

I need a program to determine that value(bridge values are subject to change)

Thanks

[phantomeye]

hey tim, i tought you were tim bryant but found out u were taufeek. i also asked this on yahoo answers, if u want 2 check them out.
http://ca.answers.yahoo.com/question/index?qid=20090316114126AAp1Suq
http://ca.answers.yahoo.com/question/index;_ylt=AjcGGiWijRMh0my.JvWGCWzAFQx.;_ylv=3?qid=20090316113825AAdqJFh