A Large Petroleum Refiner Blends Five Petroleum Products Into Three High Grade Jet Fuels. The Table Below …

       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.               Final Blend of Jet Fuel    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.           The   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.           Required:                (a) Formulate   the linear programming model for this problem.   (b) Use   Excel and Solver to solve the model.