I) Think of the network as a highway map, and assume a cost of traversing each arc. Suppose that we incur an additional cost (or penalty) of a units every time we make a left turn. Formulate this problem as a shortest path problem. Hint: Create a new network G with nodes (i- sponding to each arc (i Define appropriate arcs and are lengths to the new network G*. As an instance consider the given network, and you want to find the shortest path from node to node 12. What is G What is the shortest path and its distance on G (including a left turn penalty of a 10? 2) Let cij 20 denote the capacity of an arc in a given network. Define the capacity of a directed path P as the minimum anc capacity in P. The maximum capacity path problem is to determine a maximum capacity path from a specified source node s to every other node in the network. Modify Dijkstra's algorithm so that it solves the maximum capacity path problem. Justify your algorithm