{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Suplementares ex5","Teste PL4","teste PL5"],"read":"whole","date_system":"1900"}

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["Algoritmo Simplex Rescrito usando matrizes"]
[]
["a)"]
["variáveis básicas","x","y","f1",null,null,"variáveis não básicas","f2","f3",null,null,"Termos Independentes"]
["B",1,0,-1,null,null,"D",0,0,null,null,"b",1]
[null,0,1,0,{"$nulls":3},-1,0,{"$nulls":3},2]
[null,1,1,0,{"$nulls":3},0,1,{"$nulls":3},5]
[]
["CB",3,1,0,null,null,"CD",0,0]
[]
[]
["B-1",{"$f":"MINVERSE(B5:D7)","v":0},-1,1,null,null,"B-1.D",{"$f":"MMULT(B12:D14,H5:I7)","v":1},1,null,null,"B-1.b",{"$f":"MMULT(B12:D14,M5:M7)","v":3}]
[null,0,1,0,{"$nulls":3},-1,0,{"$nulls":3},2]
[null,-1,-1,1,{"$nulls":3},1,1,{"$nulls":3},2]
[]
["CB.B-1D",{"$f":"MMULT(B9:D9,H12:I14)","v":2},3,{"$nulls":3},"F=CB.B-1.b",{"$f":"MMULT(B9:D9,M12:M14)","v":11}]
[]
["R= -CD+CB.B-1D",{"$f":"SUM(B16,-H9)","v":2},{"$f":"SUM(C16,-I9)","v":3}]
[]
["Já é uma solução óptima pois R não tem valores negativos"]
[]
["c)"]
["variáveis básicas","x","y","f1",null,null,"variáveis não básicas","f2","f3","w",null,"Termos Independentes"]
["B",1,0,-1,null,null,"D",0,0,1,null,"b",1]
[null,0,1,0,{"$nulls":3},-1,0,2,null,null,2]
[null,1,1,0,{"$nulls":3},0,1,1,null,null,5]
[]
["CB",3,1,0,null,null,"CD",0,0,-2]
[]
[]
["B-1",{"$f":"MINVERSE(B24:D26)","v":0},-1,1,null,null,"B-1.D",{"$f":"MMULT(B31:D33,H24:J26)","v":1},1,-1,null,"B-1.b",{"$f":"MMULT(B31:D33,M24:M26)","v":3}]
[null,0,1,0,{"$nulls":3},-1,0,2,null,null,2]
[null,-1,-1,1,{"$nulls":3},1,1,-2,null,null,2]
[]
["CB.B-1D",{"$f":"MMULT(B28:D28,H31:J33)","v":2},3,-1,null,null,"F=CB.B-1.b",{"$f":"MMULT(B28:D28,M31:M33)","v":11}]
[]
["R= -CD+CB.B-1D",{"$f":"SUM(B35,-H28)","v":2},{"$f":"SUM(C35,-I28)","v":3},{"$f":"SUM(D35,-J28)","v":1}]
[]
["Já é uma solução óptima pois R não tem valores negativos"]
[]
["d)","depois de calculos elementares, f4 sai da base e f2 entra na base"]
["variáveis básicas","x","y","f1","f2",null,"variáveis não básicas","f3","f4",null,null,"Termos Independentes"]
["B",1,0,-1,0,null,"D",0,0,null,null,"b",1]
[null,0,1,0,-1,null,null,0,0,{"$nulls":3},2]
[null,1,1,0,0,null,null,1,0,{"$nulls":3},5]
[null,2,1,0,0,null,null,0,-1,{"$nulls":3},6]
[]
["CB",3,1,0,0,null,"CD",0,0]
[]
[]
["B-1",{"$f":"MINVERSE(B43:E46)","v":0},0,-1,1,null,"B-1.D",{"$f":"MMULT(B51:E54,H43:I46)","v":-1},-1,null,null,"B-1.b",{"$f":"MMULT(B51:E54,M43:M46)","v":1}]
[null,0,0,2,-1,null,null,2,1,{"$nulls":3},4]
[null,-1,0,-1,1,null,null,-1,-1,{"$nulls":3},0]
[null,0,-1,2,-1,null,null,2,1,{"$nulls":3},2]
[]
["CB.B-1D",{"$f":"MMULT(B48:E48,H51:I54)","v":-1},-2,{"$nulls":3},"F=CB.B-1.b",{"$f":"MMULT(B48:E48,M51:M54)","v":7}]
[]
["R= -CD+CB.B-1D",{"$f":"B56-H48","v":-1},{"$f":"C56-I48","v":-2}]
[]
["Já é uma solução óptima pois R não tem valores negativos"]

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["Algoritmo Simplex Rescrito usando matrizes"]
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[]
["variáveis básicas","x","y","z",null,null,"variáveis não básicas","f1","f2","f3",null,"Termos Independentes"]
["B",{"v":-1,"d":"-1.00"},{"v":3,"d":"3.00"},{"v":2,"d":"2.00"},null,null,"D",{"v":1,"d":"1.00"},{"v":0,"d":"0.00"},{"v":0,"d":"0.00"},null,"b",{"v":12,"d":"12.00"}]
[null,{"v":2,"d":"2.00"},{"v":-1,"d":"-1.00"},{"v":1,"d":"1.00"},{"$nulls":3},{"v":0,"d":"0.00"},{"v":1,"d":"1.00"},{"v":0,"d":"0.00"},null,null,{"v":7,"d":"7.00"}]
[null,{"v":1,"d":"1.00"},{"v":-2,"d":"-2.00"},{"v":1,"d":"1.00"},{"$nulls":3},{"v":0,"d":"0.00"},{"v":0,"d":"0.00"},{"v":-1,"d":"-1.00"},null,null,{"v":5,"d":"5.00"}]
[]
["CB",{"v":1,"d":"1.00"},{"v":2,"d":"2.00"},{"v":5,"d":"5.00"},null,null,"CD",{"v":0,"d":"0.00"},{"v":0,"d":"0.00"},{"v":0,"d":"0.00"}]
[]
[]
["B-1",{"$f":"MINVERSE(B5:D7)","v":-0.09999999999999999},0.7000000000000001,-0.5,null,null,"B-1.D",{"$f":"MMULT(B12:D14,H5:J7)","v":-0.09999999999999999},0.7000000000000001,0.5,null,"B-1.b",{"$f":"MMULT(B12:D14,M5:M7)","v":1.2000000000000002},null,"delta",{"$f":"M12/J12","v":2.4000000000000004}]
[null,0.1,0.3,-0.5,{"$nulls":3},0.1,0.3,0.5,null,null,0.8000000000000003,null,null,{"$f":"M13/J13","v":1.6000000000000005},"Y sai da base"]
[null,0.3,-0.1,0.5,{"$nulls":3},0.3,-0.1,-0.5,null,null,5.3999999999999995,null,null,{"$f":"M14/J14","v":-10.799999999999999}]
[]
[{"$nulls":6},"CB.B-1D",{"$f":"MMULT(B9:D9,H12:J14)","v":1.6},0.8,{"v":-1,"d":"-1.00"},null,"F=CB.B-1.b",{"$f":"MMULT(B9:D9,M12:M14)","v":{"v":29.799999999999997,"d":"29.80"}}]
[{"$nulls":6},"R= -CD+CB.B-1D",{"$f":"SUM(H16,-H9)","v":1.6},{"$f":"SUM(I16,-I9)","v":0.8},{"$f":"J16-J9","v":{"v":-1,"d":"-1.00"}}]
[]
[{"$nulls":6},"F3 entra na base."]
[]
[]
["2 iteração"]
["variáveis básicas","x","z","f3",null,null,"variáveis não básicas","f1","f2","y",null,"Termos Independentes"]
["B",{"v":-1,"d":"-1.00"},{"v":2,"d":"2.00"},{"v":0,"d":"0.00"},null,null,"D",{"v":1,"d":"1.00"},{"v":0,"d":"0.00"},{"v":3,"d":"3.00"},null,"b",{"v":12,"d":"12.00"}]
[null,{"v":2,"d":"2.00"},{"v":1,"d":"1.00"},{"v":0,"d":"0.00"},{"$nulls":3},{"v":0,"d":"0.00"},{"v":1,"d":"1.00"},{"v":-1,"d":"-1.00"},null,null,{"v":7,"d":"7.00"}]
[null,{"v":1,"d":"1.00"},{"v":1,"d":"1.00"},{"v":-1,"d":"-1.00"},{"$nulls":3},{"v":0,"d":"0.00"},{"v":0,"d":"0.00"},{"v":-2,"d":"-2.00"},null,null,{"v":5,"d":"5.00"}]
[]
["CB",{"v":1,"d":"1.00"},{"v":5,"d":"5.00"},{"v":0,"d":"0.00"},null,null,"CD",{"v":0,"d":"0.00"},{"v":0,"d":"0.00"},{"v":2,"d":"2.00"}]
[]
[]
["B-1",{"$f":"MINVERSE(B24:D26)","v":-0.2},0.4,{"v":0,"d":"0.00"},null,null,"B-1.D",{"$f":"MMULT(B31:D33,H24:J26)","v":-0.2},0.4,{"v":-1,"d":"-1.00"},null,"B-1.b",{"$f":"MMULT(B31:D33,M24:M26)","v":0.3999999999999999}]
[null,0.4,0.2,{"v":0,"d":"0.00"},{"$nulls":3},0.4,0.2,{"v":1.0000000000000002,"d":"1.00"},null,null,6.200000000000001]
[null,0.2,0.6,{"v":-1,"d":"-1.00"},{"$nulls":3},0.2,0.6,{"v":2,"d":"2.00"},null,null,1.6000000000000005]
[]
[{"$nulls":6},"CB.B-1D",{"$f":"MMULT(B28:D28,H31:J33)","v":{"v":1.8,"d":"1.80"}},{"v":1.4,"d":"1.40"},{"v":4.000000000000001,"d":"4.00"},null,"F=CB.B-1.b",{"$f":"MMULT(B28:D28,M31:M33)","v":{"v":31.400000000000006,"d":"31.40"}}]
[{"$nulls":6},"R= -CD+CB.B-1D",{"$f":"SUM(H35,-H28)","v":{"v":1.8,"d":"1.80"}},{"$f":"SUM(I35,-I28)","v":{"v":1.4,"d":"1.40"}},{"$f":"J35-J28","v":{"v":2.000000000000001,"d":"2.00"}}]
[]
[]
[]
["ex 16"]
[]
["variáveis básicas","x","y","z",null,null,"variáveis não básicas","f1","f2","f3",null,"Termos Independentes"]
["B",{"v":-1,"d":"-1.00"},{"v":3,"d":"3.00"},{"v":2,"d":"2.00"},null,null,"D",{"v":1,"d":"1.00"},{"v":0,"d":"0.00"},{"v":0,"d":"0.00"},null,"b",{"v":9,"d":"9.00"}]
[null,{"v":2,"d":"2.00"},{"v":-1,"d":"-1.00"},{"v":1,"d":"1.00"},{"$nulls":3},{"v":0,"d":"0.00"},{"v":1,"d":"1.00"},{"v":0,"d":"0.00"},null,null,{"v":7,"d":"7.00"}]
[null,{"v":1,"d":"1.00"},{"v":-2,"d":"-2.00"},{"v":1,"d":"1.00"},{"$nulls":3},{"v":0,"d":"0.00"},{"v":0,"d":"0.00"},{"v":-1,"d":"-1.00"},null,null,{"v":2,"d":"2.00"}]
[]
["CB",{"v":1,"d":"1.00"},{"v":2,"d":"2.00"},{"v":5,"d":"5.00"},null,null,"CD",{"v":0,"d":"0.00"},{"v":0,"d":"0.00"},{"v":0,"d":"0.00"}]
[]
[]
["B-1",{"$f":"MINVERSE(B43:D45)","v":-0.09999999999999999},0.7000000000000001,-0.5,null,null,"B-1.D",{"$f":"MMULT(B50:D52,H43:J45)","v":-0.09999999999999999},0.7000000000000001,0.5,null,"B-1.b",{"$f":"MMULT(B50:D52,M43:M45)","v":3},null,"delta",{"$f":"M50/J50","v":6}]
[null,0.1,0.3,-0.5,{"$nulls":3},0.1,0.3,0.5,null,null,2,null,null,{"$f":"M51/J51","v":4},"Y sai da base"]
[null,0.3,-0.1,0.5,{"$nulls":3},0.3,-0.1,-0.5,null,null,2.9999999999999996,null,null,{"$f":"M52/J52","v":-5.999999999999999}]
[]
[{"$nulls":6},"CB.B-1D",{"$f":"MMULT(B47:D47,H50:J52)","v":1.6},0.8,{"v":-1,"d":"-1.00"},null,"F=CB.B-1.b",{"$f":"MMULT(B47:D47,M50:M52)","v":{"v":22,"d":"22.00"}}]
[{"$nulls":6},"R= -CD+CB.B-1D",{"$f":"SUM(H54,-H47)","v":1.6},{"$f":"SUM(I54,-I47)","v":0.8},{"$f":"J54-J47","v":{"v":-1,"d":"-1.00"}}]
[{"$nulls":6},"F3 entra na base."]
[]
[]
["2 iteração"]
["variáveis básicas","x","z","f3",null,null,"variáveis não básicas","f1","f2","y",null,"Termos Independentes"]
["B",{"v":-1,"d":"-1.00"},{"v":2,"d":"2.00"},{"v":0,"d":"0.00"},null,null,"D",{"v":1,"d":"1.00"},{"v":0,"d":"0.00"},{"v":3,"d":"3.00"},null,"b",{"v":9,"d":"9.00"}]
[null,{"v":2,"d":"2.00"},{"v":1,"d":"1.00"},{"v":0,"d":"0.00"},{"$nulls":3},{"v":0,"d":"0.00"},{"v":1,"d":"1.00"},{"v":-1,"d":"-1.00"},null,null,{"v":7,"d":"7.00"}]
[null,{"v":1,"d":"1.00"},{"v":1,"d":"1.00"},{"v":-1,"d":"-1.00"},{"$nulls":3},{"v":0,"d":"0.00"},{"v":0,"d":"0.00"},{"v":-2,"d":"-2.00"},null,null,{"v":2,"d":"2.00"}]
[]
["CB",{"v":1,"d":"1.00"},{"v":5,"d":"5.00"},{"v":0,"d":"0.00"},null,null,"CD",{"v":0,"d":"0.00"},{"v":0,"d":"0.00"},{"v":2,"d":"2.00"}]
[]
[]
["B-1",{"$f":"MINVERSE(B61:D63)","v":-0.2},0.4,{"v":0,"d":"0.00"},null,null,"B-1.D",{"$f":"MMULT(B68:D70,H61:J63)","v":-0.2},0.4,{"v":-1,"d":"-1.00"},null,"B-1.b",{"$f":"MMULT(B68:D70,M61:M63)","v":1.0000000000000002}]
[null,0.4,0.2,{"v":0,"d":"0.00"},{"$nulls":3},0.4,0.2,{"v":1.0000000000000002,"d":"1.00"},null,null,5]
[null,0.2,0.6,{"v":-1,"d":"-1.00"},{"$nulls":3},0.2,0.6,{"v":2,"d":"2.00"},null,null,4]
[]
[{"$nulls":6},"CB.B-1D",{"$f":"MMULT(B65:D65,H68:J70)","v":{"v":1.8,"d":"1.80"}},{"v":1.4,"d":"1.40"},{"v":4.000000000000001,"d":"4.00"},null,"F=CB.B-1.b",{"$f":"MMULT(B65:D65,M68:M70)","v":{"v":26,"d":"26.00"}}]
[{"$nulls":6},"R= -CD+CB.B-1D",{"$f":"SUM(H72,-H65)","v":{"v":1.8,"d":"1.80"}},{"$f":"SUM(I72,-I65)","v":{"v":1.4,"d":"1.40"}},{"$f":"J72-J65","v":{"v":2.000000000000001,"d":"2.00"}}]

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["Algoritmo Simplex Rescrito usando matrizes"]
[]
["1) 2) 3)"]
["variáveis básicas","x","y","z",null,null,"variáveis não básicas","f1","f2","f3",null,null,"Termos Independentes"]
["B",{"v":1,"d":"1.00"},{"v":2,"d":"2.00"},{"v":-1,"d":"-1.00"},null,null,"D",{"v":-1,"d":"-1.00"},{"v":0,"d":"0.00"},{"v":0,"d":"0.00"},null,null,"b",{"v":10,"d":"10.00"}]
[null,{"v":2,"d":"2.00"},{"v":1,"d":"1.00"},{"v":1,"d":"1.00"},{"$nulls":3},{"v":0,"d":"0.00"},{"v":1,"d":"1.00"},{"v":0,"d":"0.00"},{"$nulls":3},{"v":30,"d":"30.00"}]
[null,{"v":1,"d":"1.00"},{"v":1,"d":"1.00"},{"v":1,"d":"1.00"},{"$nulls":3},{"v":0,"d":"0.00"},{"v":0,"d":"0.00"},{"v":-1,"d":"-1.00"},{"$nulls":3},{"v":15,"d":"15.00"}]
[]
["CB",{"v":3,"d":"3.00"},{"v":2,"d":"2.00"},{"v":1,"d":"1.00"},null,null,"CD",{"v":0,"d":"0.00"},{"v":0,"d":"0.00"},{"v":0,"d":"0.00"}]
[]
[]
["B-1",{"$f":"MINVERSE(B5:D7)","v":0},1,-1,null,null,"B-1.D",{"$f":"MMULT(B12:D14,H5:J7)","v":0},1,1,null,null,"B-1.b",{"$f":"MMULT(B12:D14,N5:N7)","v":{"v":15,"d":"15.00"}},null,"delta",{"$f":"N12/J12","v":15}]
[null,0.3333333333333333,-0.6666666666666666,1,{"$nulls":3},-0.3333333333333333,-0.6666666666666666,-1,{"$nulls":3},{"v":-1.6666666666666679,"d":"-1.67"},null,null,{"$f":"N13/J13","v":1.6666666666666679},"Y sai da base"]
[null,-0.3333333333333333,-0.33333333333333337,1,{"$nulls":3},0.3333333333333333,-0.33333333333333337,-1,{"$nulls":3},{"v":1.6666666666666643,"d":"1.67"},null,null,{"$f":"N14/J14","v":-1.6666666666666643}]
[]
[{"$nulls":6},"CB.B-1D",{"$f":"MMULT(B9:D9,H12:J14)","v":-0.3333333333333333},1.3333333333333335,{"v":0,"d":"0.00"},null,null,"F=CB.B-1.b",{"$f":"MMULT(B9:D9,N12:N14)","v":{"v":43.33333333333333,"d":"43.33"}}]
[{"$nulls":6},"R= -CD+CB.B-1D",{"$f":"SUM(H16,-H9)","v":-0.3333333333333333},{"$f":"SUM(I16,-I9)","v":1.3333333333333335},{"$f":"J16-J9","v":{"v":0,"d":"0.00"}}]
[]
["testar a base y,f1,f3"]
["variáveis básicas","y","f1","f3",null,null,"variáveis não básicas","f2","x","z",null,null,"Termos Independentes"]
["B",{"v":2,"d":"2.00"},{"v":-1,"d":"-1.00"},{"v":0,"d":"0.00"},null,null,"D",{"v":0,"d":"0.00"},{"v":1,"d":"1.00"},{"v":-1,"d":"-1.00"},null,null,"b",{"v":10,"d":"10.00"},"Beta",160]
[null,{"v":1,"d":"1.00"},{"v":0,"d":"0.00"},{"v":0,"d":"0.00"},{"$nulls":3},{"v":1,"d":"1.00"},{"v":2,"d":"2.00"},{"v":1,"d":"1.00"},{"$nulls":3},{"v":30,"d":"30.00"}]
[null,{"v":1,"d":"1.00"},{"v":0,"d":"0.00"},{"v":-1,"d":"-1.00"},{"$nulls":3},{"v":0,"d":"0.00"},{"v":1,"d":"1.00"},{"v":1,"d":"1.00"},{"$nulls":3},{"v":15,"d":"15.00"}]
[]
["CB",{"v":2,"d":"2.00"},{"v":0,"d":"0.00"},{"v":0,"d":"0.00"},null,null,"CD",{"v":0,"d":"0.00"},{"v":3,"d":"3.00"},{"v":1,"d":"1.00"}]
[]
[]
["B-1",{"$f":"MINVERSE(B21:D23)","v":{"v":0,"d":"0.00"}},{"v":1,"d":"1.00"},{"v":0,"d":"0.00"},null,null,"B-1.D",{"$f":"MMULT(B28:D30,H21:J23)","v":{"v":1,"d":"1.00"}},{"v":2,"d":"2.00"},{"v":1,"d":"1.00"},null,null,"B-1.b",{"$f":"MMULT(B28:D30,N21:N23)","v":{"v":30,"d":"30.00"}}]
[null,{"v":-1,"d":"-1.00"},{"v":2,"d":"2.00"},{"v":0,"d":"0.00"},{"$nulls":3},{"v":2,"d":"2.00"},{"v":3,"d":"3.00"},{"v":3,"d":"3.00"},{"$nulls":3},{"v":50,"d":"50.00"}]
[null,{"v":0,"d":"0.00"},{"v":1,"d":"1.00"},{"v":-1,"d":"-1.00"},{"$nulls":3},{"v":1,"d":"1.00"},{"v":1,"d":"1.00"},{"v":0,"d":"0.00"},{"$nulls":3},{"v":15,"d":"15.00"}]
[]
[{"$nulls":6},"CB.B-1D",{"$f":"MMULT(B25:D25,H28:J30)","v":{"v":2,"d":"2.00"}},{"v":4,"d":"4.00"},{"v":2,"d":"2.00"},null,null,"F=CB.B-1.b",{"$f":"MMULT(B25:D25,N28:N30)","v":{"v":60,"d":"60.00"}}]
[{"$nulls":6},"R= -CD+CB.B-1D",{"$f":"SUM(H32,-H25)","v":{"v":2,"d":"2.00"}},{"$f":"SUM(I32,-I25)","v":{"v":1,"d":"1.00"}},{"$f":"J32-J25","v":{"v":1,"d":"1.00"}}]
[]
[]
[]
["4) e 5)"]
["testar a base y,f1,f3"]
["variáveis básicas","y","f1","f3",null,null,"variáveis não básicas","f2","x","z","w",null,"Termos Independentes"]
["B",{"v":2,"d":"2.00"},{"v":-1,"d":"-1.00"},{"v":0,"d":"0.00"},null,null,"D",{"v":0,"d":"0.00"},{"v":1,"d":"1.00"},{"v":-1,"d":"-1.00"},{"v":2,"d":"2.00"},null,"b",{"v":10,"d":"10.00"}]
[null,{"v":1,"d":"1.00"},{"v":0,"d":"0.00"},{"v":0,"d":"0.00"},{"$nulls":3},{"v":1,"d":"1.00"},{"v":2,"d":"2.00"},{"v":1,"d":"1.00"},{"v":2,"d":"2.00"},null,null,{"v":30,"d":"30.00"}]
[null,{"v":1,"d":"1.00"},{"v":0,"d":"0.00"},{"v":-1,"d":"-1.00"},{"$nulls":3},{"v":0,"d":"0.00"},{"v":1,"d":"1.00"},{"v":1,"d":"1.00"},{"v":3,"d":"3.00"},null,null,{"v":15,"d":"15.00"}]
[]
["CB",{"v":2,"d":"2.00"},{"v":0,"d":"0.00"},{"v":0,"d":"0.00"},null,null,"CD",{"v":0,"d":"0.00"},{"v":3,"d":"3.00"},{"v":1,"d":"1.00"},{"v":5,"d":"5.00"}]
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