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A petroleum company produces three grades of motor oil-super, premium, and extra-from three components. The company wants to determine the optimal mix of the three components in each grade of motor oil that will maximize profit. The maximum quantities available of each component and their cost per barrel are as follows: To ensure the appropriate blend, each grade has certain general specifications. Each grade must have a minimum amount of component 1 plus a combination of other components, as follows: The company wants to produce at least 3,000 barrels of each grade of motor oil. The solution is x1sx2sx3sx1px2px1ex2ex3eZ=1,500bbl.=600bbl.=900bbl.=1,200bbl.=1,800bbl.=1,800bbl.=300bbl.=900bbl.=$76,800 Summarizing these results, 3,000 barrels of super grade, premium, and extra are produced. Also, 4,500 barrels of component 1 , and 2,700 barrels of component 2, and 1,800 barrels of component 3 are used. (This problem also contains multiple optimal solutions.)