4 The diagram represents a map of an army truck-driving course that includes several bridges. The start and a 'safe point' just after each bridge have been given (stage; state) labels. The number below each bridge shows its weight limit, in tonnes.
\includegraphics[max width=\textwidth, alt={}, center]{1ceb5585-6d3f-4723-ad49-7addfb40ab66-4_698_1413_438_365} An army cadet needs to drive a truck through the course from start to finish, crossing exactly three bridges.

1. Draw a network, using the (stage; state) labels given, to represent the routes through the course. The weights on the arcs should show the weight limits for the bridges. The cadet wants to find out the weight of the heaviest truck she can use.
2. Which network problem does she need to solve?
3. Set up a dynamic programming tabulation to solve the cadet's problem. Write down the weight of the heaviest truck she can use and write down the (stage; state) labels for the route she should take.