4 Origin 5 Well 1 6 Well 1 Mobile Galveston 7 Well 2 Mobile 8 Well 2 A 1 Oil transport 2 3 Network formulation B Destination Cost per 1000 barrels F G H J K M N Flow balance constraints Flow (1000s of barrels) Location Flow in Supply Total LHS Flow out Demand Total RHS $10 Well 1 150 150 0 0 $13 Well 2 0 200 200 0 0 0 $15 Mobile 0 0 0 0 0 0 9 Mobile 10 Galveston 11 Mobile 12 Mobile 13 Galveston 14 Galveston LA 15 NY 16 LA Galveston Galveston Mobile $12 Galveston 0 0 0 0 0 0 $6 NY 0 0 0 0 140 140 $6 LA 0 0 0 160 160 355353 NY $16 LA $17 NY $14 $16 LA $15 NY $15 17 18 19 20 21 22 23 24 25 26 Total cost 0 27 28 Sunco Oil collects oil from two wells. Well 1 can produce up to 150,000 barrels per day, and Well 2 can produce up to 200,000 barrels per day. Once oil is collected from a well, it is shipped to refineries in Mobile and Galveston. After the oil is processed at the refineries, it is shipped to New York and Los Angeles. Assume that no oil is lost during the refining process; in other words, if 1,000 barrels enter the refinery, 1,000 barrels leave the refinery. New York requires 140,000 barrels of oil per day, and Los Angeles requires 160,000 barrels per day. Shipment costs between various locations are given in oil.xlsx. (If a cost is not given for a particular pair of locations, this means that oil is not shipped between these locations.) a) Draw a picture of Sunco's shipping network. Label all nodes, arcs, supplies, demands, and costs. b) Formulate an optimization problem that minimizes Sunco's total cost while satisfying demand. Write your model in NPS format and Clearly define your decision variables, objective function, constraints, and parameters. c) Using oil.xlsx as a template, implement an Excel model that optimizes Sunco's shipping routes. Your model should meet demands at New York and Los Angeles at minimum total cost. Note that once again, the network is not balanced as given (i.e., total supply does not equal total demand). Remember to submit your Excel model via Sakai. d) Suppose you want to model costs incurred by using the refineries at Mobile and Galveston, in addition to the transportation costs you are already modeling. For instance, maybe it costs $18 to refine 1000 barrels of oil at Mobile, and $20 to refine 1000 barrels of oil at Galveston. How can your network flow model be modified to reflect these costs? Hint: There are multiple ways to do this. One way involves adding two nodes to your network. Think about having a "front door" and a "back door" for each of your refineries. Assume that only unrefined oil can be transported between refineries, and only refined oil can be transported to New York and Los Angeles.