3. Logistics company ABC has received a request to ship containers from point O to point T. Their traffic manager has identified potential transshipment points (A, B, C, D, and E) and worked out a network diagram. The network is illustrated in the figure below. An edge between two points indicates that transportation is allowed between them. The number associated with the edge is the distance (in 1,000 miles) between the points. 4 E 7 1 3 5 12 . B 2 2 5 . D 7 a. Find a shortest path from point O to point T. Please work out the solution manually. [10] b. After obtaining the shortest path in Question 3 (a), the traffic manager realizes that the company wishes to minimize the total transportation cost instead of the total transportation distance. He learns from his colleague that the unit transportation cost is $4,136. He claims that the shortest path found in Question 3 (a) is also a path which minimizes the total transportation cost. Is his claim correct? Please justify your answer. [5] C. The manager has just realized that there were errors in their information system such that the distances between points in the network were incorrect. He has found that the length of every edge consistently missed the same constant distance. In other words, the actual distance of every edge shall be the one shown in the graph plus the same constant. He claims that, since the same value must be added to the distance associated with every edge to fix the errors, the shortest path in Question 3 (a) shall remain optimal after the errors are fixed. Is his claim correct? Please justify your answer. [5]