The Conch Oil Company needs to transport 30 million barrels of crude oil from a port in Doha, Qatar in the Persian Gulf to three refineries throughout Europe. The refineries are in Rotterdam, Netherlands; Toulon, France; and Palermo, Italy, and require 6 million, 15 million, and 9 million barrels, respectively. The oil can be transported to the refineries in three different ways. First, oil may be shipped from Qatar to Rotterdam, Toulon, and Palermo on supertankers traveling around Africa at costs of $1.20, $1.40, and $1.35 per barrel, respectively. Conch is contractually obligated to send at least 25% of its oil via these supertankers. Alternatively, oil can be shipped from Doha to Suez, Egypt, at a cost of $0.35 per barrel, then through the Suez Canal to Port Said at a cost of $0.20 per barrel, then from Port Said to Rotterdam, Toulon, and Palermo at per barrel costs of $0.27, $0.23, and $0.19, respectively. Finally, up to 15 million barrels of the oil shipped from Doha to Suez can then be sent via pipeline Damietta, Egypt, at $0.16 per barrel. From Damietta, it can shipped to Rotterdam, Toulon, and Palermo at costs of $0.25, $0.20, and $0.15, respectively.

a. Draw a network flow model for this problem.

b. Implement your model in a spreadsheet and solve it.

c. What is the optimal solution?