$35.00 LPP Using Excel Solver - A large petroleum refiner blends five petroleum products into three high grade jet fuels ...
Found in Mathematics: Linear-SystemsChapter 1, # 0
Q:A large petroleum refiner blends five petroleum products into three high grade jet fuels. The table below summarizes the very precise recipes for the three jet fuels, the cost and availability information for the five component petroleum products, and the wholesale price per gallon of each jet fuel blend. The numbers in the body of the table indicate the percentages each petroleum product contributes to the volume of each jet fuel. For example, petroleum product 2 should comprise 15 percent of jet fuel 1.
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Petroleum 1 2 3 Cost per Gal Max Avail/Week Product 1 20 10 30 $2.50 50,000 Gallons 2 15 40 10 $2.75 40,000 Gallons 3 30 20 10 $2.25 30,000 Gallons 4 10 10 20 $3.00 10,000 Gallons 5 25 20 30 $3.50 20,000 Gallons Wholesale Price/Gal $6.50 $7.50 $7.00 Weekly processing capacity of 125,000 gallons cannot be exceeded. There is no problem selling the final blends of jet fuel, although minimum weekly production levels of 20,000, 20,000 and 10,000 gallons, respectively, have been established for the three final blends.
he refiner wishes to determine the number of gallons of each petroleum product to use in each jet fuel blend so as to maximize total weekly profit.
In making these decisions, you must assure that the blending specifications (percentages) are met, that total weekly production does not exceed the plant capacity, and that you do not exceed the availability of each component petroleum product.
Let xij equal the number of gallons of petroleum product i used in jet fuel blend j.
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Required: (a) Formulate the linear programming model for this problem. (b) Use Excel and Solver to solve the model.
