Round up to 4 d.p.

2. (l 1 marks] A company needs to transport some goods from their plant in Shenzhen to a customer in Beijing. The network diagram below shows possible routes and their respective shipping costs per unit (in RMB}. Node 1 represents Shenzhen and node 8 represents Beijing. Node 2 to node 7 represents some other cities. The objective is to nd the cheapest route for the shipment. (a) Using Dijkstra Algorithm, one obtains a permanent label for each node. (i) Complete the table below with the permanent labels produced in the algorithm. Node 1 2 3 4 5 6 7 E (ii) Find the cheapest route for the shipment. {iii} Find the lowest total shipping cost per unit. (b) To solve the problem as a linear program, defme the decision variables as follows: x-- : {1 if the arc from node 1' to node j is on the cheapest route U l] otherwise {i} Find the constraints associated with the Node 6 and Node 3. {ii} Complete the table below with the indicated coordinates of the optimal solution