3. (24 marks) An oil company has two refineries at locations 1 and 2 with a monthly supply of 12,000 barrels and 13,000 barrels respectively. The barrels are shipped to one of the three warehouses at locations A, B and C and then to one of the three destinations at locations P, Q and R. The monthly demands of these three destinations are 6,000, 6,500 and 8,000 barrels, respectively. All possible shipping routes and the corresponding shipping costs per barrel are shown in the table below. to A B P Q R from 1 5 6 11 2 4 3 7 A 4 8 7 B 5 6 C 7.5 k Each blank cell in the table indicates the corresponding shipping route does not exist. (a) Draw a complete network representation of the problem. Label the nodes with 1, 2, A, B, C, P, Q and R. (b) (c) The objective is to minimize the total shipping cost. Let xi; be the number of units shipped from node i to node j. Find the constraint associated with each node. In addition to the constraints above, there are other constraints shown below. Find a mathematical description for each of them. Constraint I II Description Shipment from location 1 to B cannot be more than 4,000 barrels. P cannot receive more barrels directly from location 1 than from the warehouse(s) III A cannot handle more than 8,000 barrels at a time. IV B cannot handle more than 9,500 barrels at a time. V C cannot handle more than 7,000 barrels at a time