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Posted on Jul 28, 2024

Part II. Sensitivity Analysis in LP Consult the LINDO output to answer the questions below A refinery takes four type of raw gasoline, blends them,

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Part II. Sensitivity Analysis in LP Consult the LINDO output to answer the questions below A refinery takes four type of raw gasoline, blends them, and produces three types of fuel Raw Gasoline 1 2 Available (barrels/day) 4200 5550 7900 Price (S/barrel) 30.55 35.11 38.73 Octane Rating 65 88 91 3 4 98 4800 40.15 1/5 Selling Price (S/barrels) 50.71 Demand (barrels/day) 8,000 Any amount can be sold Minimum Fuel Blend TypeOctane Rating 1 93 47.55 2 91 86 45.99 13,000 Raw gasoline not used in blending can be sold at $40.95/barrel if octane rating 2 90 $38.85/barrel if octane rating 2) -28 X11 3) - 21 X13 2 X23 5 X33 12 X43 X11 X12 X13 Yi 9) 8000 10) 13000 END LINDO Output LP OPTIMUM FOUND AT STEP OB JECTIVE FUNCTION VALUE 1) 235674.2 VARIABLE VALUE REDUCED COST 0.000000 0.000000 X21 3900.892822 0.000000 0.000000 3900.892822 0.000000 0.000000 X31 X41 0.000000 0.000000 X12 0.000000 0.000000 0.000000 X22 2.045990 X32 2.312857 X42 2.935549 2551.785645 1649.107178 0.000000 x13 X23 0.000000 X43 7900.000000 0.000000 0.000000 0.000000 899.107117 1648.214233 0.000000 0.000000 9.742143 Y2 Y3 Y4 8.912857 0.000000 11.877857 DUAL PRICES ROW SLACK OR SURPLUS 2) 3) 0.000000 0.423571 0.00000 0.334615 4) 0.0000 -0.423571 5) 0.0000 8.300000 6) 0.000000 13.482142 7) 0.000000 11.132857 8) 9) 0.000000 12.677857 198.214279 0.000000 10) 0.000000 -1.755000 NO. ITERATIONS= 8 RANGES IN WHICH THE BASIS IS UNCHANGED: OBJ COEFFICIENT RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE INCREASE COEF DECREASE X11 20.160000 0.000001 INFINITY x21 15.600000 NINIT 0.000000 X31 11.980000 0.000001 INFINITY 0.000002 X41 10.560000 0.000000 X12 17.000000 10.903472 8.700000 X22 12.440000 2.045989 INFINITY 8.820000 INFINITY X32 2.312858 X42 7-400000 2.935550 INFINITY X13 15.440000 7.020000 0.000000 X23 10.880000 0.000000 3.471981 X33 7.260000 INFINITY 0.000001 5.840000 0.000000 X43 0.000002 8.300000 8-700000 7.020000 3.740000 INFINITY INFINITY INEIITY 2 9.742143 2.220000 Y3 8.912857 Y4 0.800000 11.877857 RIGHTHAND SIDE RANGES ROW CURRENT ALLOWABLE ALLOWABLE DECREASE RHS INCREASE 0.000000 10945.651367 5549.999512 0.000000 0.000000 42853.570312 0.000000 71449.992188 5549.999512 4200.000000 INFINITY 1648.214233 6 5550.000000 241.304337 2798.484863 7 7900.000000 4800.000000 8000.000000 13000.000000 213.461533 168.181808 7900.000000 2189.130371 INFINITY 198.214279 10 6592.856934 264.285706 THE TABLEAU X22 ROW (BASIS) X11 X21 X31 X41 X12 2.046 0.411 0.000 1 ART 0.000 0.000 0.000 0.000 3.300 0.700 0.000 0.000 2 X21 1.000 0.000 0.000 3 X12 0.000 0.000 1.000 0.115 0.000 4 X13 1.000 0.000 0.000 0.000 0.179 1.000 -0.700 33 0.000 0.000 0.000 0.000 0.000 -3.300 0.000 0.000 0.000 6 X23 0.589 7 X41 -2.300 0.000 0.300 1.000 0.000 0.411 X43 2.300 0.000 0.000 -0.300 0.000 0.000 0-411 SLK 9 9 0.000 0.000 0.000 0.000 -0.821 10 0.000 0.000 0.000 0.000 0.000 0.063 X32 X33 ROW X42 X13 X23 X43 2.313 0.000 0.000 0.000 2.936 0.000 0.000 0.000 0.000 0.000 0.000 0.464 0.000 0.589 -0.269 0.000 0.000 0.000 0.000 0.000 2 3 0.000 0.000 -0.071 0.179 1.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 -0.464 -0.589 0.000 1.000 0.000 0.000 0.464 0.589 0.000 0.000 0.000 0.000 0.000 0.000 0.000 8 -0.464 0.411 0.000 0.000 1.000 0.000 0.000 0.000 -1.179 9 -0.929 0.000 0.000 0.000 1.000 10 0.071 0.091 0.000 0.000 0.000 SLK 3 ROW Y2 3 Y4 SLK 2 SLK 4 SLK 5 1 9.742 8.913 11.878 0.424 0.335 0.424 8.300 2 0.411 0.464 0.589 0.118 0.000 0.018 0.000 0.000 3 0.000 0.000 0.000 0.000 0.038 0.000 4 -0.179 -0.071 0.179 0.036 0.000 0.036 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.589 0.411 0.464 0.464 -0.589 -0.118 0.000 -0.018 0.000 0.000 0.000 0.082 7 0.589 0.000 0.018 0.411 -1.179 -0.411 0.464 0.082 0.000 -0.018 0.821 -0.929 -0.036 0.000 -0.036 0.000 -0.038 10 0.179 0.071 0.179 -0.036 -0.036 1.000 4/5 ROW SLK 6 SLK 7 SLK 8 SLK 9 SLK 10 RHS 11.133 1.755 13.482 12.678 0.000 0.24E+06 0.411 0.464 0.589 0.000 0.375 3900.893 3 0.000 0.000 0.000 0.000 0.000 0.000 4 -0.179 0.071 0.179 0.000 -0.250 2551.786 7900.000 1649.107 0.000 1.000 0.000 0.000 0.000 0.589 -0.464 -0.589 0.000 -0.375 0.375 0.375 0.411 0.464 0.589 0.000 0.000 3900.893 899.107 8 -0.411 -0.464 0.411 -0.929 -1.179 198.214 -0.821 1.000 -0.750 0.179 0.071 0.250 10 -0-179 0.000 1648.214 Part II. Sensitivity Analysis in LP Consult the LINDO output to answer the questions below A refinery takes four type of raw gasoline, blends them, and produces three types of fuel Raw Gasoline 1 2 Available (barrels/day) 4200 5550 7900 Price (S/barrel) 30.55 35.11 38.73 Octane Rating 65 88 91 3 4 98 4800 40.15 1/5 Selling Price (S/barrels) 50.71 Demand (barrels/day) 8,000 Any amount can be sold Minimum Fuel Blend TypeOctane Rating 1 93 47.55 2 91 86 45.99 13,000 Raw gasoline not used in blending can be sold at $40.95/barrel if octane rating 2 90 $38.85/barrel if octane rating 2) -28 X11 3) - 21 X13 2 X23 5 X33 12 X43 X11 X12 X13 Yi 9) 8000 10) 13000 END LINDO Output LP OPTIMUM FOUND AT STEP OB JECTIVE FUNCTION VALUE 1) 235674.2 VARIABLE VALUE REDUCED COST 0.000000 0.000000 X21 3900.892822 0.000000 0.000000 3900.892822 0.000000 0.000000 X31 X41 0.000000 0.000000 X12 0.000000 0.000000 0.000000 X22 2.045990 X32 2.312857 X42 2.935549 2551.785645 1649.107178 0.000000 x13 X23 0.000000 X43 7900.000000 0.000000 0.000000 0.000000 899.107117 1648.214233 0.000000 0.000000 9.742143 Y2 Y3 Y4 8.912857 0.000000 11.877857 DUAL PRICES ROW SLACK OR SURPLUS 2) 3) 0.000000 0.423571 0.00000 0.334615 4) 0.0000 -0.423571 5) 0.0000 8.300000 6) 0.000000 13.482142 7) 0.000000 11.132857 8) 9) 0.000000 12.677857 198.214279 0.000000 10) 0.000000 -1.755000 NO. ITERATIONS= 8 RANGES IN WHICH THE BASIS IS UNCHANGED: OBJ COEFFICIENT RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE INCREASE COEF DECREASE X11 20.160000 0.000001 INFINITY x21 15.600000 NINIT 0.000000 X31 11.980000 0.000001 INFINITY 0.000002 X41 10.560000 0.000000 X12 17.000000 10.903472 8.700000 X22 12.440000 2.045989 INFINITY 8.820000 INFINITY X32 2.312858 X42 7-400000 2.935550 INFINITY X13 15.440000 7.020000 0.000000 X23 10.880000 0.000000 3.471981 X33 7.260000 INFINITY 0.000001 5.840000 0.000000 X43 0.000002 8.300000 8-700000 7.020000 3.740000 INFINITY INFINITY INEIITY 2 9.742143 2.220000 Y3 8.912857 Y4 0.800000 11.877857 RIGHTHAND SIDE RANGES ROW CURRENT ALLOWABLE ALLOWABLE DECREASE RHS INCREASE 0.000000 10945.651367 5549.999512 0.000000 0.000000 42853.570312 0.000000 71449.992188 5549.999512 4200.000000 INFINITY 1648.214233 6 5550.000000 241.304337 2798.484863 7 7900.000000 4800.000000 8000.000000 13000.000000 213.461533 168.181808 7900.000000 2189.130371 INFINITY 198.214279 10 6592.856934 264.285706 THE TABLEAU X22 ROW (BASIS) X11 X21 X31 X41 X12 2.046 0.411 0.000 1 ART 0.000 0.000 0.000 0.000 3.300 0.700 0.000 0.000 2 X21 1.000 0.000 0.000 3 X12 0.000 0.000 1.000 0.115 0.000 4 X13 1.000 0.000 0.000 0.000 0.179 1.000 -0.700 33 0.000 0.000 0.000 0.000 0.000 -3.300 0.000 0.000 0.000 6 X23 0.589 7 X41 -2.300 0.000 0.300 1.000 0.000 0.411 X43 2.300 0.000 0.000 -0.300 0.000 0.000 0-411 SLK 9 9 0.000 0.000 0.000 0.000 -0.821 10 0.000 0.000 0.000 0.000 0.000 0.063 X32 X33 ROW X42 X13 X23 X43 2.313 0.000 0.000 0.000 2.936 0.000 0.000 0.000 0.000 0.000 0.000 0.464 0.000 0.589 -0.269 0.000 0.000 0.000 0.000 0.000 2 3 0.000 0.000 -0.071 0.179 1.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 -0.464 -0.589 0.000 1.000 0.000 0.000 0.464 0.589 0.000 0.000 0.000 0.000 0.000 0.000 0.000 8 -0.464 0.411 0.000 0.000 1.000 0.000 0.000 0.000 -1.179 9 -0.929 0.000 0.000 0.000 1.000 10 0.071 0.091 0.000 0.000 0.000 SLK 3 ROW Y2 3 Y4 SLK 2 SLK 4 SLK 5 1 9.742 8.913 11.878 0.424 0.335 0.424 8.300 2 0.411 0.464 0.589 0.118 0.000 0.018 0.000 0.000 3 0.000 0.000 0.000 0.000 0.038 0.000 4 -0.179 -0.071 0.179 0.036 0.000 0.036 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.589 0.411 0.464 0.464 -0.589 -0.118 0.000 -0.018 0.000 0.000 0.000 0.082 7 0.589 0.000 0.018 0.411 -1.179 -0.411 0.464 0.082 0.000 -0.018 0.821 -0.929 -0.036 0.000 -0.036 0.000 -0.038 10 0.179 0.071 0.179 -0.036 -0.036 1.000 4/5 ROW SLK 6 SLK 7 SLK 8 SLK 9 SLK 10 RHS 11.133 1.755 13.482 12.678 0.000 0.24E+06 0.411 0.464 0.589 0.000 0.375 3900.893 3 0.000 0.000 0.000 0.000 0.000 0.000 4 -0.179 0.071 0.179 0.000 -0.250 2551.786 7900.000 1649.107 0.000 1.000 0.000 0.000 0.000 0.589 -0.464 -0.589 0.000 -0.375 0.375 0.375 0.411 0.464 0.589 0.000 0.000 3900.893 899.107 8 -0.411 -0.464 0.411 -0.929 -1.179 198.214 -0.821 1.000 -0.750 0.179 0.071 0.250 10 -0-179 0.000 1648.214