ALUMNO: JESUS ASMETH PEREZ CAMACHO ING.SISTEMAS COMPUTACIONALESGAUSS-SEIDEL1.- Una compaa de electrnica produce transistores, resistores y chips de computadora. Cada resistor requiere cuatro unidades de cobre, una de zinc y dos de vidrio. Cada resistor requiere tres, tres y una unidades de dichos materiales respectivamente y cada chip de computadora requiere dos, una y tres respectivamente. En forma de tabla, esta informacin queda as;ComponenteCobreZincVidrio

Transistores412

Resistores331

Chips de computadora213

Los suministros de estos materiales varan de una semana a la otra, de modo que la compaa necesita determinar una corrida de produccin diferente cada semana. Por ejemplo las cantidades disponibles de materiales son 960 unidades de cobre, 510 unidades de zinc y 610 unidades de vidrio. Plantee el sistema de ecuaciones que modela la corrida de produccin y utilice Excel y la informacin que se da en este captulo sobre la solucin de ecuaciones algebraicas lineales con Excel pera resolver cual es el nmero de transistores, resistores y chips de computadora por manufacturar esta semana.GAUSS-SEIDEL

DEFINIMOS LAS ECUACIONES:

4t+3r+2c=960

t+3r+c=510

2t+r+3c=610

DESPEJAMOS LAS VARIABLES

ITERACIONtrcError

1100100100

2115103.333333103.33333313.04%

3110.833333397.222222292.2222222-3.76%

4120.9722222102.31481597.0370378.38%

5114.745370497.330246988.5802469-5.43%

6122.7121914102.22479494.39300416.49%

7116.134902397.631601587.4502743-5.66%

8123.0511617102.13827493.3661985.62%

9116.713195297.860880187.253134-5.43%

10122.9777729102.01122492.90424325.09%

11117.039460798.03932887.3444102-5.07%

12122.7982989101.87204392.62725024.69%

13117.282342698.191483687.510453-4.70%

14122.6011608101.73573592.41461044.34%

15117.490893798.328076387.6873146-4.35%

16122.4102855101.60726492.23004544.02%

17117.679529498.45322387.8573884-4.02%

18122.2313885101.48769492.06257273.72%

19117.852943198.568679688.0165096-3.72%

20122.0652355101.37684991.90847813.45%

21118.013124198.675428888.1642266-3.43%

22121.9113151101.27421691.76610773.20%

23118.161283998.774192488.3010511-3.17%

24121.7688301101.17922291.63441332.96%

25118.298377198.865585588.427706-2.93%

26121.6369578101.09130691.51255342.74%

27118.425244198.950162988.5449262-2.71%

28121.5149147101.00994391.3997832.54%

29118.542651199.028434188.6534091-2.51%

30121.4019699100.93464791.29542122.36%

31118.651304499.100869688.7538046-2.32%

32121.2974455100.86496491.19884052.18%

33118.75185799.167904788.8467151-2.14%

34121.2007139100.80047691.10946042.02%

35118.844912899.229941988.9326987-1.98%

36121.1111942100.74079691.02674421.87%

37118.931030899.287353989.0122718-1.83%

38121.0283487100.68556690.95019491.73%

39119.010728299.340485589.0859123-1.70%

40120.9516798100.63445390.87935271.60%

41119.084483899.389655889.1540624-1.57%

42120.8807269100.58715190.81379221.49%

43119.152740599.435160389.2171316-1.45%

44120.815064100.54337690.75311961.38%

45119.215908299.477272189.2754987-1.34%

46120.7542965100.50286490.69697051.27%

47119.274366599.516244389.3295142-1.24%

48120.6980597100.46537390.64500761.18%

49119.328466499.552310989.3795025-1.15%

50120.6460155100.43067790.59691881.09%

51119.378532999.585688689.425764-1.06%

52120.5978516100.39856890.55241521.01%

53119.424866699.616577789.4685764-0.98%

54120.5532785100.36885290.51122970.94%

55119.467745999.645163989.5081969-0.91%

56120.5120286100.34135290.47311480.87%

57119.507428399.671618989.5448634-0.84%

58120.4738541100.31590390.43784150.80%

59119.544152299.696101589.5787963-0.78%

60120.4385257100.2923590.40519810.74%

61119.578138199.718758789.6101993-0.72%

62120.4058313100.27055490.37498840.69%

63119.609590299.739726889.6392611-0.67%

64120.3755744100.25038390.34703090.64%

65119.638697399.759131689.6661561-0.62%

66120.3475733100.23171690.32115790.59%

67119.665634499.777089689.691046-0.57%

68120.3216598100.2144490.29721390.55%

69119.690563299.793708889.7140802-0.53%

70120.2976783100.19845290.2750550.50%

71119.713633499.809088989.735397-0.49%

72120.2754848100.18365790.25454810.47%

73119.734983599.823322489.7551246-0.45%

74120.2549459100.16996490.23557020.43%

75119.754741999.836494689.7733814-0.42%

76120.2359383100.15729290.21800720.40%

77119.773027399.848684889.790277-0.39%

78120.2183479100.14556590.20175360.37%

79119.789949399.859966289.805913-0.36%

80120.2020688100.13471390.18671170.34%

81119.805609799.870406589.8203833-0.33%

82120.1870035100.12466990.17279140.32%

83119.820102699.880068489.8337747-0.31%

84120.1730614100.11537490.15990880.29%

85119.833514999.889009989.8461676-0.28%

86120.1601587100.10677290.14798680.27%

87119.845927299.897284889.8576367-0.26%

88120.148218100.09881290.13695360.25%

89119.857414299.904942889.8682506-0.24%

90120.1371676100.09144590.12674290.23%

91119.868044799.912029889.8780733-0.22%

92120.126941100.08462790.11729360.22%

93119.877882799.918588589.8871636-0.21%

94120.1174769100.07831890.10854870.20%

95119.886987299.924658189.8955761-0.19%

96120.1087183100.07247990.10045580.18%

97119.895412999.930275389.9033615-0.18%

98120.1006128100.06707590.09296630.17%

99119.903210599.935473689.9105664-0.16%

100120.0931116100.06207490.08603510.16%

101119.910426699.940284489.9172342-0.15%

102120.0861696100.05744690.07962080.15%

103119.917104899.944736689.9234048-0.14%

104120.0797452100.05316390.07368460.14%

105119.923285199.948856789.9291154-0.13%

106120.0737997100.049290.0681910.13%

107119.929004699.952669789.9344002-0.12%

108120.0682976100.04553290.0631070.12%

109119.934297799.956198589.939291-0.11%

110120.0632056100.04213790.0584020.11%

111119.939196299.959464189.9438172-0.10%

112120.0584933100.03899690.05404790.10%

113119.943729499.962486389.948006-0.10%

114120.0541323100.03608890.05001830.09%

115119.947924799.965283189.9518824-0.09%

116120.0500965100.03339890.04628920.09%

117119.951807299.967871589.9554698-0.08%

118120.0463615100.03090890.04283810.08%

119119.955400299.970266889.9587898-0.08%

120120.042905100.02860390.03964420.07%

121119.958725499.972483689.9618622-0.07%

122120.0397062100.02647190.03668860.07%

123119.961802699.974535189.9647056-0.06%

124120.0367459100.02449790.03395320.06%

125119.964650499.976433689.967337-0.06%

126120.0340063100.02267190.03142180.06%

127119.967285999.978190689.9697722-0.06%

128120.0314709100.02098190.02907920.05%

129119.96972599.979816689.9720258-0.05%

La iteracion 120 es la que mas se aproxima a 0%

es decir:

Numero de transistores 120.031471 120 transistores

Numero de resistores 100.020981 100 resistores

Numero de chips 90.0290792 90 chips

GAUSS SIMPLE2.- Un ingeniero elctrico supervisa la produccin de tres tipos de componentes elctricos. Para ello se requieren tres clases de material: metal, plstico y caucho. A continuacin se presentan las cantidades necesarias para producir cada componente.

ComponenteMetal g/componentePlstico g/componenteHule g/componente

115.301.0

217.401.2

319.551.5

Si cada da se dispone de un total de 3.89, 0.095 y 0.282 Kg. de metal, plstico y caucho, respectivamente, Cuntos componentes produce por da?1kg=1000g3.89kg=3890g0.095kg=95g0.282kg=282g

GAUSS SIMPLE

XYZ

(1517193890)

0.30.40.5595

11.21.5282

(11.21.5282)

0.30.40.5595R2=-.3*R1+R2

1517193890R3=-15*R1+R3

(11.21.5282)

00.040.110.4

0-1-3.5-340R3=1/.04*R2+R3

(11.21.5282)

00.040.110.4

00-1-80

SUSTITUCIONES:

-Z=-80

Z=80

0.04Y+0.1(80)=10.4

0.04Y+8=10.4

X+1.2(60)+1.5(80)=282

X+192=282

X=282-192

X=90

RESPUESTA

COMPONENTE 1 =90

COMPONENTE 2=60

COMPONENTE 3=80

COMPONENTE AL DIA 230