PROBLEM I The Black Gold, Inc. oil company owns two refineries, say refinery A and refinery B. Refinery A is capable of producing 20 barrels of gasoline and 25 barrels of fuel oil per day; refinery B is capable of producing 40 barrels of gasoline and 20 barrels of fuel oil per day. The company requires at least 1,000 barrels of gasoline and at least 800 barrels of fuel oil. It costs $300 per day to operate refinery A and $500 per day to operate refinery B. (a) Formulate an LP that Black Gold, Inc. can use to determine the number of days to operate each refinery in order to minimize costs. (b) Solve the LP you formulated in part (a) using the method of your choice. (c) Suppose that the cost per day to operate refinery B is changed from the constant $500 per day to $c per day. For what values of the parameter e does the current solution remain optimal? (d) Suppose that the company requires b barrels of gasoline per day, where b is a parameter. For what values of 6 does the current basis remain optimal? (e) Compute the shadow price of the gasoline constraint.