Find the optimum flow on the network below by applying the network simplex algorithm (Cij, uij). (4,50) (2,40) 01-20 (4,30) 4 D4=15 (2,50) (5,10) 3 D3=5 • Guidelines: You can collaborate or compare your assignment with a classmate, but everyone must submit his/her own assignment. You should also note your classmate's name. You are expected to construct an initial feasible solution to start the algorithm. However, you should avoid using a near-optimal solution to terminate the algorithm in a short time by observing the problem parameters. To get full credit, you must implement the algorithm for at least two iterations from beginning to end.

5.01-1. Dijkstra's Algorithm (1, part 1). Consider the network shown below, and Dijkstra's link-stat algorithm to find the least cost path from source node U to all other destinations. Using the algorithm statement and its visual representation used in the textbook, complete the first row in the table below showing the link state algorithm's execution by matching the table entries (a), (b), (c), an (d) with their values. Write down your final [correct] answer, as you'll need it for the next question. Step 0 (a) (b) (c) (d) 3 8 V 2 X N' u 4 2 6 -W 3 D(v),p(v) D(v).p(v) (a) 1 SZ 1 W X D(w),p(w) D(x).p(x) (b) (c) [Choose ] [Choose ] 5,x 6,v 3,u 4,v 1,u 8,u 2,u infinity 7,u [Choose ] Z D(y).p(y) D(z).p(z) (d) ∞

Q- In order to plot a graph of f(x)=z and g(y)=z in the same graph, with t as a parameter. The function used is plot3(x,y,z) O plot(x,y,z) O surf(x,y,z) O mesh(z) O

4. For the graph below: 5 2 1 20 14 a. What is the shortest route from 0 to 3? What is the shortest route from 0 to 8? (Route length is the sum of the weights of the edges in the route. When no weight is assigned to an edge the weight is assumed to be 1.) b. What is the shortest route from 5 to 2? What is the shortest route from 5 to 5 to 2? c. What is the shortest route from 7 to 2? From 7 to 0?