# A company owns two refineries in Dallas and New York. The company can purchase two types of crude…

A company owns two refineries in Dallas and New York. The company can purchase two types of crude oil: light crude oil, and heavy crude oil at the prices of \$15 and \$10 per barrel, respectively. Because of shortages, the maximum amounts of these crudes that can be purchased are 3 million and 2 million barrels, respectively. The following quantities of gasoline, kerosene, and jet fuel are produced per barrel of each type of oil:

Note that 5 percent and 8 percent of the light and heavy crude are lost during the refining process, respectively. The company has contracted to deliver these products to three consumers in Kansas City, Los Angeles, and Detroit. The demands of these products are given below:

It is desired to find the amounts that must be purchased by the company of each crude type at each of its refining facilities, and the shipping pattern of the products to Kansas City, Los Angeles, and Detroit that satisfy the demands and minimize the total cost (purchase plus shipping). The shipping and handling of a barrel of any finished product from the refineries to the consumers is given below:

a. Formulate the problem.

b. Suggest a decomposition scheme for solving the problem.

c. Solve the problem using your scheme in Part (b).

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