![S5
S1 S4
TONS/DIA Au g/t Ag g/t %Fe %Pb %Zn %As %Cu S7 S9
1790.00 S1: Alim Flot 9.5 9.447 4.25 0.23 0.6
165.93 S3: Conc WA 86.5 95.79 30.64 3.88 1.66
1626.79 S4: Rel WA 0.6 1.65 1.48 0.02 0.1 S3
1807.37 S7: Rel WB 0.58 2.55 1.5 0.02 0.22 S6
185.43 S5: Conc WC 2.44 1.9 3.67 0.07 0.59
1621.95 S9: Rel WC 0.27 4.5 1.28 0.01 0.22
2.12 S8: Conc Cl 25.6 21.441 12.17 0.54 5.85
2.72 S2: Rel Cl 0.68 6.897 4.46 0.11 0.72
4.84 S6:Conc WB 9.63 10.747 28.4 0.2 1.71 S2
S8
Ω31 77.000 86.343 26.390 3.650 1.060 0.000 0.000
Ω32 85.82 88.89 26.18 3.77 0.94 0.00 0.00
Ω43 -85.90 -94.14 -29.16 -3.86 -1.56 0.00 0.00
Ω64 9.03 9.10 26.92 0.18 1.61 0.00 0.00
Ω75 -1.860 0.650 -2.170 -0.050 -0.370 0.000 0.000
Ω56 -7.19 -8.85 -24.73 -0.13 -1.12 0.00 0.00 16,886.007 -16,969.509 0.000 449.757 S1+S2 = S3+S4
Ω57 1.86 -0.65 2.17 0.05 0.37 0.00 0.00 -16,969.509456 18,650.466 -69.904 -1,463.036 S4+S5=S6+S7
Ω95 -2.17 2.60 -2.39 -0.06 -0.37 0.00 0.00 0.000 -69.904 17.461 50.655 S7=S5+S9
Ω28 -24.920 -14.544 -7.710 -0.430 -5.130 0.000 0.000 449.757 -1,463.036 50.655 1,410.202 S6=S2+S8
Ω86 15.97 10.69 -16.23 0.34 4.14 0.00 0.00
Ω68 -15.97 -10.69 16.23 -0.34 -4.14 0.00 0.00 0.0012869 0.0012423 0.0027072 0.0007812 -14989.07540 Φ2 0.00151691
0.0012423 0.0012577 0.0026783 0.0008124 15527.90502 Φ4 0.90881954
0.0027072 0.0026783 0.0697009 -0.0005885 0 Φ7 1.00970665
0.0007812 0.0008124 -0.0005885 0.0013240 0 Φ9 0.90611571
TONS/DIA
Φ2 0.001516908 S1 1790
Φ4 0.908819543 S2 2.715265576 ratio
S6/S4 Φ7 1.009706655 S3 165.9282827 10.65140941
Φ9 0.906115711 S4 1626.786983 9.9314
Φ1 1 S5 185.4277891 ratio operación
Φ3 0.092697365 S6 4.839860237 7.5000
Φ5 0.103590944 S7 1807.374912
Φ6 0.002703833 S8 2.124594662
Φ8 0.001186924 S9 1621.947123
-S8/S2
fact ponder. Au Ag Fe Pb Zn As Cu
W1 1 1 0 0 0 #?DIV/0! #?DIV/0!
W2 219 2 0 1 0 #?DIV/0! #?DIV/0! % W(i) = 100/[Ley(%) · (100 ?Ley(%))]?
W3 1 6 0 0 0 #?DIV/0! #?DIV/0! gr/tn W(i) = 1000000/[Ley(%) · (100 ?Ley(%))]?
W4 281 38 0 25 1 #?DIV/0! 1
W5 18 29 0 2 0 #?DIV/0! #?DIV/0!
W6 1 1 0 0 0 #?DIV/0! #?DIV/0!
W7 301 16 0 25 0 #?DIV/0! 1
W8 0 0 0 0 0 #?DIV/0! #?DIV/0!
W9 1379 5 0 100 0 #?DIV/0! 1
A mayores valores, mayor influencia de dicho elemento en el cálculo
Para el Au Para el Ag Para el Fe Para el Pb
-0.75 0.00 0.00 0.00 -0.75 0.02 0.00 0.00 -2219.67 175.60 0.00 0.00 -17.25 0.03 0.00 0.00
0.00 -0.01 0.00 0.00 0.02 -0.09 -0.06 0.00 175.60 -411.87 -235.97 0.30 0.03 -0.08 -0.05 0.00
0.00 0.00 0.00 0.00 0.00 -0.06 -0.21 0.00 0.00 -235.97 -367.07 0.00 0.00 -0.05 -0.05 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06 0.00 0.30 0.00 -222.58 0.00 0.00 0.00 -0.04
Para el Zn Para el As Para el Cu
-38.68 0.82 0.00 0.00 #?DIV/0! #?DIV/0! 0.00 #?DIV/0! #?DIV/0! 0.83 0.00 #?DIV/0!
0.82 -6.11 -5.28 0.00 #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! 0.83 #?DIV/0! #?DIV/0! #?DIV/0!
0.00 -5.28 -9.24 0.00 0.00 #?DIV/0! #?DIV/0! 0.00 0.00 #?DIV/0! #?DIV/0! 0.00
0.00 0.00 0.00 -4.92 #?DIV/0! #?DIV/0! 0.00 #?DIV/0! #?DIV/0! #?DIV/0! 0.00 #?DIV/0!
Para el Au Para el Ag Para el Fe Para el Pb
-1.33096949 -1.129610751 0.983209429 -0.00184633 -1.337203749 -0.437835267 0.128986758 -6.69268E-05 -0.000475928 -0.000321214 0.000206493 -4.4518E-07 -0.058061688 -0.047912959 0.04065951 -3.81503E-05
-1.12961075 -289.8471315 252.2819764 -0.47269762 -0.437835267 -15.19698807 4.477049624 -0.001630159 -0.000321214 -0.004060289 0.002610162 -5.52038E-06 -0.047912959 -25.0269767 21.2381924 -0.017866083
0.983209429 252.2819764 -437.291037 0.411434428 0.128986758 4.477049624 -5.970900654 0.000480247 0.000206493 0.002610162 -0.004402224 3.54878E-06 0.040659512 21.23819242 -36.465113 0.015161372
-0.00184633 -0.472697616 0.411434428 -294.544973 -6.69268E-05 -0.001630159 0.000480247 -15.88295859 -4.4518E-07 -5.52038E-06 3.54878E-06 -0.004492786 -3.81503E-05 -0.017866083 0.01516137 -24.50536813
Para el Zn Para el As Para el Cu
-0.02599862 -0.006939118 0.003967364 -3.5362E-06 #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0!
-0.00693912 -0.325645237 0.186184046 -0.00013694 #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0!
0.003967364 0.186184046 -0.21469394 7.8294E-05 #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0!
-3.5362E-06 -0.00013694 7.8294E-05 -0.20337113 #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0!
Errores debido a las leyes
Au Ag Fe Pb Zn As Cu Au Ag Fe Pb Zn As Cu
ΔM1 0.937 -0.922 0.071 -0.148 0.356 0.000 0.000 2ΔM1 1.875 -1.843 0.143 -0.295 0.713 0.000 0.000
ΔM2 0.186 -0.907 0.134 0.005 -0.075 0.000 0.000 2ΔM2 0.373 -1.815 0.268 0.009 -0.150 0.000 0.000
ΔM3 0.088 -1.700 -0.025 0.004 -0.038 0.000 0.000 2ΔM3 0.176 -3.399 -0.051 0.008 -0.077 0.000 0.000
ΔM4 -0.005 -0.007 0.056 0.000 -0.003 0.000 0.000 2ΔM4 -0.011 -0.014 0.111 -0.001 -0.007 0.000 0.000
Multiplicadores de lagrange
Au Ag Fe Pb Zn As Cu
λ1 -2.74 2.82 0.00 0.02 -0.02 #?DIV/0! #?DIV/0!
λ2 -65.65 13.17 0.00 -0.06 0.03 #?DIV/0! #?DIV/0!
λ3 18.73 11.93 0.00 -0.10 -0.01 #?DIV/0! #?DIV/0!
λ4 3.06 0.22 0.00 0.01 0.00 #?DIV/0! #?DIV/0!
CALCULO DE FLUJOS NORMALIZADOS EN UN CIRCUITO DE FLOTACI?N DE 4 ETAPAS
CORRECCI?N DE LEYES POR MULTIPLICADORES DE LAGRANGE
1 2 3
4](https://image.slidesharecdn.com/calculodeflujosnormalizadosenuncircuitodeflotacion-131010202248-phpapp02/85/Calculo-de-flujos-normalizados-en-un-circuito-de-flotacion-1-320.jpg)
Calculo de flujos normalizados en un circuito de flotacion
- 1. S5 S1 S4 TONS/DIA Au g/t Ag g/t %Fe %Pb %Zn %As %Cu S7 S9 1790.00 S1: Alim Flot 9.5 9.447 4.25 0.23 0.6 165.93 S3: Conc WA 86.5 95.79 30.64 3.88 1.66 1626.79 S4: Rel WA 0.6 1.65 1.48 0.02 0.1 S3 1807.37 S7: Rel WB 0.58 2.55 1.5 0.02 0.22 S6 185.43 S5: Conc WC 2.44 1.9 3.67 0.07 0.59 1621.95 S9: Rel WC 0.27 4.5 1.28 0.01 0.22 2.12 S8: Conc Cl 25.6 21.441 12.17 0.54 5.85 2.72 S2: Rel Cl 0.68 6.897 4.46 0.11 0.72 4.84 S6:Conc WB 9.63 10.747 28.4 0.2 1.71 S2 S8 Ω31 77.000 86.343 26.390 3.650 1.060 0.000 0.000 Ω32 85.82 88.89 26.18 3.77 0.94 0.00 0.00 Ω43 -85.90 -94.14 -29.16 -3.86 -1.56 0.00 0.00 Ω64 9.03 9.10 26.92 0.18 1.61 0.00 0.00 Ω75 -1.860 0.650 -2.170 -0.050 -0.370 0.000 0.000 Ω56 -7.19 -8.85 -24.73 -0.13 -1.12 0.00 0.00 16,886.007 -16,969.509 0.000 449.757 S1+S2 = S3+S4 Ω57 1.86 -0.65 2.17 0.05 0.37 0.00 0.00 -16,969.509456 18,650.466 -69.904 -1,463.036 S4+S5=S6+S7 Ω95 -2.17 2.60 -2.39 -0.06 -0.37 0.00 0.00 0.000 -69.904 17.461 50.655 S7=S5+S9 Ω28 -24.920 -14.544 -7.710 -0.430 -5.130 0.000 0.000 449.757 -1,463.036 50.655 1,410.202 S6=S2+S8 Ω86 15.97 10.69 -16.23 0.34 4.14 0.00 0.00 Ω68 -15.97 -10.69 16.23 -0.34 -4.14 0.00 0.00 0.0012869 0.0012423 0.0027072 0.0007812 -14989.07540 Φ2 0.00151691 0.0012423 0.0012577 0.0026783 0.0008124 15527.90502 Φ4 0.90881954 0.0027072 0.0026783 0.0697009 -0.0005885 0 Φ7 1.00970665 0.0007812 0.0008124 -0.0005885 0.0013240 0 Φ9 0.90611571 TONS/DIA Φ2 0.001516908 S1 1790 Φ4 0.908819543 S2 2.715265576 ratio S6/S4 Φ7 1.009706655 S3 165.9282827 10.65140941 Φ9 0.906115711 S4 1626.786983 9.9314 Φ1 1 S5 185.4277891 ratio operación Φ3 0.092697365 S6 4.839860237 7.5000 Φ5 0.103590944 S7 1807.374912 Φ6 0.002703833 S8 2.124594662 Φ8 0.001186924 S9 1621.947123 -S8/S2 fact ponder. Au Ag Fe Pb Zn As Cu W1 1 1 0 0 0 #?DIV/0! #?DIV/0! W2 219 2 0 1 0 #?DIV/0! #?DIV/0! % W(i) = 100/[Ley(%) · (100 ?Ley(%))]? W3 1 6 0 0 0 #?DIV/0! #?DIV/0! gr/tn W(i) = 1000000/[Ley(%) · (100 ?Ley(%))]? W4 281 38 0 25 1 #?DIV/0! 1 W5 18 29 0 2 0 #?DIV/0! #?DIV/0! W6 1 1 0 0 0 #?DIV/0! #?DIV/0! W7 301 16 0 25 0 #?DIV/0! 1 W8 0 0 0 0 0 #?DIV/0! #?DIV/0! W9 1379 5 0 100 0 #?DIV/0! 1 A mayores valores, mayor influencia de dicho elemento en el cálculo Para el Au Para el Ag Para el Fe Para el Pb -0.75 0.00 0.00 0.00 -0.75 0.02 0.00 0.00 -2219.67 175.60 0.00 0.00 -17.25 0.03 0.00 0.00 0.00 -0.01 0.00 0.00 0.02 -0.09 -0.06 0.00 175.60 -411.87 -235.97 0.30 0.03 -0.08 -0.05 0.00 0.00 0.00 0.00 0.00 0.00 -0.06 -0.21 0.00 0.00 -235.97 -367.07 0.00 0.00 -0.05 -0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06 0.00 0.30 0.00 -222.58 0.00 0.00 0.00 -0.04 Para el Zn Para el As Para el Cu -38.68 0.82 0.00 0.00 #?DIV/0! #?DIV/0! 0.00 #?DIV/0! #?DIV/0! 0.83 0.00 #?DIV/0! 0.82 -6.11 -5.28 0.00 #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! 0.83 #?DIV/0! #?DIV/0! #?DIV/0! 0.00 -5.28 -9.24 0.00 0.00 #?DIV/0! #?DIV/0! 0.00 0.00 #?DIV/0! #?DIV/0! 0.00 0.00 0.00 0.00 -4.92 #?DIV/0! #?DIV/0! 0.00 #?DIV/0! #?DIV/0! #?DIV/0! 0.00 #?DIV/0! Para el Au Para el Ag Para el Fe Para el Pb -1.33096949 -1.129610751 0.983209429 -0.00184633 -1.337203749 -0.437835267 0.128986758 -6.69268E-05 -0.000475928 -0.000321214 0.000206493 -4.4518E-07 -0.058061688 -0.047912959 0.04065951 -3.81503E-05 -1.12961075 -289.8471315 252.2819764 -0.47269762 -0.437835267 -15.19698807 4.477049624 -0.001630159 -0.000321214 -0.004060289 0.002610162 -5.52038E-06 -0.047912959 -25.0269767 21.2381924 -0.017866083 0.983209429 252.2819764 -437.291037 0.411434428 0.128986758 4.477049624 -5.970900654 0.000480247 0.000206493 0.002610162 -0.004402224 3.54878E-06 0.040659512 21.23819242 -36.465113 0.015161372 -0.00184633 -0.472697616 0.411434428 -294.544973 -6.69268E-05 -0.001630159 0.000480247 -15.88295859 -4.4518E-07 -5.52038E-06 3.54878E-06 -0.004492786 -3.81503E-05 -0.017866083 0.01516137 -24.50536813 Para el Zn Para el As Para el Cu -0.02599862 -0.006939118 0.003967364 -3.5362E-06 #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! -0.00693912 -0.325645237 0.186184046 -0.00013694 #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! 0.003967364 0.186184046 -0.21469394 7.8294E-05 #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! -3.5362E-06 -0.00013694 7.8294E-05 -0.20337113 #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! #?DIV/0! Errores debido a las leyes Au Ag Fe Pb Zn As Cu Au Ag Fe Pb Zn As Cu ΔM1 0.937 -0.922 0.071 -0.148 0.356 0.000 0.000 2ΔM1 1.875 -1.843 0.143 -0.295 0.713 0.000 0.000 ΔM2 0.186 -0.907 0.134 0.005 -0.075 0.000 0.000 2ΔM2 0.373 -1.815 0.268 0.009 -0.150 0.000 0.000 ΔM3 0.088 -1.700 -0.025 0.004 -0.038 0.000 0.000 2ΔM3 0.176 -3.399 -0.051 0.008 -0.077 0.000 0.000 ΔM4 -0.005 -0.007 0.056 0.000 -0.003 0.000 0.000 2ΔM4 -0.011 -0.014 0.111 -0.001 -0.007 0.000 0.000 Multiplicadores de lagrange Au Ag Fe Pb Zn As Cu λ1 -2.74 2.82 0.00 0.02 -0.02 #?DIV/0! #?DIV/0! λ2 -65.65 13.17 0.00 -0.06 0.03 #?DIV/0! #?DIV/0! λ3 18.73 11.93 0.00 -0.10 -0.01 #?DIV/0! #?DIV/0! λ4 3.06 0.22 0.00 0.01 0.00 #?DIV/0! #?DIV/0! CALCULO DE FLUJOS NORMALIZADOS EN UN CIRCUITO DE FLOTACI?N DE 4 ETAPAS CORRECCI?N DE LEYES POR MULTIPLICADORES DE LAGRANGE 1 2 3 4
- 2. Sabemos: Au Ag Fe Pb Zn As Cu ΔL1 1.013751365 -1.03214104 0.136281926 -0.044796646 0.316476035 #?DIV/0! #?DIV/0! ΔL2 2.0081E-05 -0.00081364 -0.00046345 -3.63151E-06 0.000743874 #?DIV/0! #?DIV/0! ΔL3 -0.173362125 0.021262653 -0.34454497 1.096852538 -0.219790811 #?DIV/0! #?DIV/0! ΔL4 0.101674618 -0.1238338 0.10646162 0.001324041 -0.021435941 #?DIV/0! #?DIV/0! ΔL5 0.247654401 -0.00222426 0.143677973 -0.001011473 -0.067753652 #?DIV/0! #?DIV/0! ΔL6 -0.070351241 0.016108084 -0.04278842 -0.000371139 0.010721324 #?DIV/0! #?DIV/0! ΔL7 -0.141644511 0.038535296 -0.24460389 0.000805612 0.092506943 #?DIV/0! #?DIV/0! ΔL8 0.006591135 0.00036897 -0.00339788 0.000223381 0.00252008 #?DIV/0! #?DIV/0! ΔL9 0.00615269 0.998484658 0.068931218 -0.000433798 -0.018672413 #?DIV/0! #?DIV/0! Sabemos leyes sin corregir Leyes corregidas Au g/t Ag g/t %Fe %Pb %Zn %As %Cu Au g/t Ag g/t %Fe %Pb %Zn %As %Cu S1 9.5 9.447 4.25 0.23 0.6 0 0 S1 8.49 10.48 4.11 0.27 0.28 #?DIV/0! #?DIV/0! S2 0.68 6.897 4.46 0.11 0.72 0 0 S2 0.68 6.90 4.46 0.11 0.72 #?DIV/0! #?DIV/0! S3 86.5 95.79 30.64 3.88 1.66 0 0 S3 86.67 95.77 30.98 2.78 1.88 #?DIV/0! #?DIV/0! S4 0.6 1.65 1.48 0.02 0.1 0 0 S4 0.50 1.77 1.37 0.02 0.12 #?DIV/0! #?DIV/0! S5 2.44 1.9 3.67 0.07 0.59 0 0 S5 2.19 1.90 3.53 0.07 0.66 #?DIV/0! #?DIV/0! S6 9.63 10.747 28.4 0.2 1.71 0 0 S6 9.70 10.73 28.44 0.20 1.70 #?DIV/0! #?DIV/0! S7 0.58 2.55 1.5 0.02 0.22 0 0 S7 0.72 2.51 1.74 0.02 0.13 #?DIV/0! #?DIV/0! S8 25.6 21.441 12.17 0.54 5.85 0 0 S8 25.59 21.44 12.17 0.54 5.85 #?DIV/0! #?DIV/0! S9 0.27 4.5 1.28 0.01 0.22 0 0 S9 0.26 3.50 1.21 0.01 0.24 #?DIV/0! #?DIV/0! S5 S1 S4 TONS/DIA Au g/t Ag g/t %Fe %Pb %Zn %As %Cu S7 S9 1790.00 S1 8.49 10.48 4.11 0.27 0.28 #?DIV/0! #?DIV/0! 1.79 S2 0.68 6.90 4.46 0.11 0.72 #?DIV/0! #?DIV/0! 152.17 S3 86.67 95.77 30.98 2.78 1.88 #?DIV/0! #?DIV/0! S3 1639.62 S4 0.50 1.77 1.37 0.02 0.12 #?DIV/0! #?DIV/0! 359.29 S5 2.19 1.90 3.53 0.07 0.66 #?DIV/0! #?DIV/0! S6 48.51 S6 9.70 10.73 28.44 0.20 1.70 #?DIV/0! #?DIV/0! 1950.41 S7 0.72 2.51 1.74 0.02 0.13 #?DIV/0! #?DIV/0! 46.72 S8 25.59 21.44 12.17 0.54 5.85 #?DIV/0! #?DIV/0! 1591.11 S9 0.26 3.50 1.21 0.01 0.24 #?DIV/0! #?DIV/0! S2 S8 Ω31 78.187 85.290 26.871 2.508 1.596 #?DIV/0! #?DIV/0! Ω32 85.99 88.87 26.52 2.67 1.16 #?DIV/0! #?DIV/0! Ω43 -86.18 -93.99 -29.61 -2.76 -1.76 #?DIV/0! #?DIV/0! Ω64 9.20 8.96 27.07 0.18 1.58 #?DIV/0! #?DIV/0! Ω75 -1.471 0.609 -1.782 -0.052 -0.530 #?DIV/0! #?DIV/0! Ω56 -7.51 -8.83 -24.92 -0.13 -1.04 #?DIV/0! #?DIV/0! 16,888.092 -16,975.517 0.000 426.216 S1+S2 = S3+S4 Ω57 1.47 -0.61 1.78 0.05 0.53 #?DIV/0! #?DIV/0! -16,975.517 18,667.622 -56.306 -1,454.619 S4+S5=S6+S7 Ω95 -1.93 1.60 -2.32 -0.06 -0.42 #?DIV/0! #?DIV/0! 0.000 -56.306 11.417 42.122 S7=S5+S9 Ω28 -24.913 -14.543 -7.713 -0.430 -5.128 #?DIV/0! #?DIV/0! 426.216 -1,454.619 42.122 1,398.764 S6=S2+S8 Ω86 15.89 10.71 -16.27 0.34 4.15 #?DIV/0! #?DIV/0! Ω68 -15.89 -10.71 16.27 -0.34 -4.15 #?DIV/0! #?DIV/0! 0.0013073 0.0012622 0.0032083 0.0008177 -15016.06354 Φ2 -0.003149053 0.0012622 0.0012770 0.0031695 0.0008480 15550.23699 Φ4 0.904233597 0.0032083 0.0031695 0.1064950 -0.0008885 0 Φ7 1.109957949 0.0008177 0.0008480 -0.0008885 0.0013743 0 Φ9 0.907875861 TONS/DIA Φ2 0.001000 S1 1790 Φ4 0.915989 S2 1.79 ratio de calculo S6/S4 Φ7 1.089612 S3 152.1698928 8.999999999 Φ9 0.888889 S4 1639.620107 Φ1 1 S5 359.2939402 0.0000 minimizando con solver Φ3 0.085011113 S6 48.50899613 Φ5 0.200722872 S7 1950.405051 ratio operación Φ6 0.027099998 S8 46.71899613 9.0000 Φ8 0.026099998 S9 1591.111111 RECALCULANDO LOS FLUJOS CON LAS LEYES CORREGIDAS Y MINIMIZANDO EL RATIO DE CONCENTRACION CON SOLVER 1 2 3 4