Consider the following network below. All questions refer to this network unless otherwise stated. If the numbers on the arcs represent the length of the arc, use the algorithm given in lectures and class notes to find the minimal spanning network, that is the network such that all points are joined at the shortest total length. You MUST use the algorithm to get points but you may check your answer by inspection. What is the total length of the minimal spanning tree 2. Use the shortest route algorithm for acyclic networks given in class (notes) to find the shortest route from node 1 to node 5. You MUST use the algorithm to get points but you may check your answer by inspection. 3. If the numbers along the arcs are considered as capacities (say of water flow), determine, using the maximal flow algorithm provided in class and lecture notes the maximal flow along the network. You MUST use the algorithm to get points but you may check your answer by inspection. 4. For the network in Figure 18 on page 429 of your text (Winston), use the annealing algorithm (start with 0 on si andon all other nodes) described in class to obtain the shortest route from node so to node si (The numbers on the ares in the diagram should be taken as lengths for the purpose of this problem.) 5. For the network in Figure 18 on page 429 of your text (Winston), use the maximum flow algorithm shown in lectures to obtain the maximal flow along the network. (The numbers on the arcs in the diagram should be taken as capacities for the purpose of this problem.)