A vehicle should drive from the start to the end node through the street network depicted in the graph on the next page. The numbers given at each edge quantify the time it takes to drive from one node to the other. The driving direction at all edges is from left to right. Each node can be allocated to one stage, as also depicted in the graph. The time optimal route from start to end is to be found through dynamic programming.

a$)$ For each node, calculate the minimum time it takes to get from this node to the terminal $($end$)$ node. For this, go backwards from the last to the first stage.

b$)$ Based on your findings from a$),$ name the quickest route through the network.

ages