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1.1

3 puntos
Apartado 1Bloques A+C

Responder a uno de los siguientes problemas (1.1, 1.2):

En una industria alimentaria se planifica la supervisión que se va a realizar a los lotes producidos el próximo mes. Se han establecido dos protocolos de revisión, la revisión normal y la exhaustiva. Los recursos humanos y materiales de esa supervisión limitan el número de lotes que se pueden revisar. Se sabe que una revisión exhaustiva de un lote consume 66 horas del departamento de envasado y 22 horas en el de etiquetado, mientras que una revisión normal de un lote consume 33 horas del departamento de envasado y 1,51{,}5 horas en el de etiquetado. En esta planificación de la supervisión se fija que, como mínimo, 55 revisiones deben ser exhaustivas y, al menos la mitad, con el protocolo normal. Se disponen de un máximo de 180180 horas en el departamento de envasado y un máximo de 8080 horas en el de etiquetado.
a
Determinar el sistema de restricciones y representar la región factible, utilizando técnicas de programación lineal.1,5 pts
b
Determinar, utilizando técnicas de programación lineal, cuál es el número máximo total de revisiones normales y exhaustivas que se pueden realizar con los recursos disponibles, así como el número de ambas revisiones para las que se alcanza este máximo.1,5 pts

Formulario

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Distribución NormalF(x)=12π∫−∞xe−12t2 dtF(x)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{x} e^{-\frac{1}{2}t^2}\,dt
Campana de la distribución normal rotulada F(x), con el área sombreada desde menos infinito hasta x, situado a la derecha de 0.
0,000,010,020,030,040,050,060,070,080,09
0,00,50000,50400,50800,51200,51600,51990,52390,52790,53190,5359
0,10,53980,54380,54780,55170,55570,55960,56360,56750,57140,5753
0,20,57930,58320,58710,59100,59480,59870,60260,60640,61030,6141
0,30,61790,62170,62550,62930,63310,63680,64060,64430,64800,6517
0,40,65540,65910,66280,66640,67000,67360,67720,68080,68440,6879
0,50,69150,69500,69850,70190,70540,70880,71230,71570,71900,7224
0,60,72570,72910,73240,73570,73890,74220,74540,74860,75170,7549
0,70,75800,76110,76420,76730,77040,77340,77640,77940,78230,7852
0,80,78810,79100,79390,79670,79950,80230,80510,80780,81060,8133
0,90,81590,81860,82120,82380,82640,82890,83150,83400,83650,8389
1,00,84130,84380,84610,84850,85080,85310,85540,85770,85990,8621
1,10,86430,86650,86860,87080,87290,87490,87700,87900,88100,8830
1,20,88490,88690,88880,89070,89250,89440,89620,89800,89970,9014
1,30,90320,90490,90660,90820,90990,91150,91310,91470,91620,9177
1,40,91920,92070,92220,92360,92510,92650,92790,92920,93060,9318
1,50,93320,93450,93570,93700,93820,93940,94060,94180,94290,9441
1,60,94520,94630,94740,94840,94950,95050,95150,95250,95350,9545
1,70,95540,95640,95730,95820,95910,95990,96080,96160,96250,9633
1,80,96410,96490,96560,96640,96710,96780,96860,96930,96990,9706
1,90,97130,97190,97260,97320,97380,97440,97500,97560,97610,9767
2,00,97720,97780,97830,97880,97930,97980,98030,98080,98120,9817
2,10,98210,98260,98300,98340,98380,98420,98460,98500,98540,9857
2,20,98610,98640,98680,98710,98750,98780,98810,98840,98870,9890
2,30,98930,98960,98980,99010,99040,99060,99090,99110,99130,9916
2,40,99180,99200,99220,99250,99270,99290,99310,99320,99340,9936
2,50,99380,99400,99410,99430,99450,99460,99480,99490,99510,9952
2,60,99530,99550,99560,99570,99590,99600,99610,99620,99630,9964
2,70,99650,99660,99670,99680,99690,99700,99710,99720,99730,9974
2,80,99740,99750,99760,99770,99770,99780,99790,99790,99800,9981
2,90,99810,99820,99820,99830,99840,99840,99850,99850,99860,9986
3,00,99870,99870,99870,99880,99880,99890,99890,99890,99900,9990
3,10,99900,99910,99910,99910,99920,99920,99920,99920,99930,9993
3,20,99930,99930,99940,99940,99940,99940,99940,99950,99950,9995
3,30,99950,99950,99950,99960,99960,99960,99960,99960,99960,9997
3,40,99970,99970,99970,99970,99970,99970,99970,99970,99970,9998
3,50,99970,99970,99980,99980,99980,99980,99980,99980,99980,9998
3,60,99980,99980,99990,99990,99990,99990,99990,99990,99990,9999
Distribución Binomialp(X=r)=(nr)pr(1−p)n−rp(X=r)=\binom{n}{r}p^r(1-p)^{n-r}
nnpp0,010,050,100,150,200,250,301/31/30,350,400,450,490,50
rr
200,98010,90250,81000,72250,64000,56250,49000,44440,42250,36000,30250,26010,2500
10,01980,09500,18000,25500,32000,37500,42000,44440,45500,48000,49500,49980,5000
20,00010,00250,01000,02250,04000,06250,09000,11110,12250,16000,20250,24010,2500
300,97030,85740,72900,61410,51200,42190,34300,29630,27460,21600,16640,13270,1250
10,02940,13540,24300,32510,38400,42190,44100,44440,44360,43200,40840,38230,3750
20,00030,00710,02700,05740,09600,14060,18900,22220,23890,28800,33410,36740,3750
30,00000,00010,00100,00340,00800,01560,02700,03700,04290,06400,09110,11760,1250
400,96060,81450,65610,52200,40960,31640,24010,19750,17850,12960,09150,06770,0625
10,03880,17150,29160,36850,40960,42190,41160,39510,38450,34560,29950,26000,2500
20,00060,01350,04860,09750,15360,21090,26460,29630,31050,34560,36750,37470,3750
30,00000,00050,00360,01150,02560,04690,07560,09880,11150,15360,20050,24000,2500
40,00000,00000,00010,00050,00160,00390,00810,01230,01500,02560,04100,05760,0625
500,95100,77380,59050,44370,32770,23730,16810,13170,11600,07780,05030,03450,0313
10,04800,20360,32810,39150,40960,39550,36020,32920,31240,25920,20590,16570,1563
20,00100,02140,07290,13820,20480,26370,30870,32920,33640,34560,33690,31850,3125
30,00000,00110,00810,02440,05120,08790,13230,16460,18110,23040,27570,30600,3125
40,00000,00000,00050,00220,00640,01460,02840,04120,04880,07680,11280,14700,1563
50,00000,00000,00000,00010,00030,00100,00240,00410,00530,01020,01850,02820,0313
600,94150,73510,53140,37710,26210,17800,11760,08780,07540,04670,02770,01760,0156
10,05710,23210,35430,39930,39320,35600,30250,26340,24370,18660,13590,10140,0938
20,00140,03050,09840,17620,24580,29660,32410,32920,32800,31100,27800,24360,2344
30,00000,00210,01460,04150,08190,13180,18520,21950,23550,27650,30320,31210,3125
40,00000,00010,00120,00550,01540,03300,05950,08230,09510,13820,18610,22490,2344
50,00000,00000,00010,00040,00150,00440,01020,01650,02050,03690,06090,08640,0938
60,00000,00000,00000,00000,00010,00020,00070,00140,00180,00410,00830,01380,0156
700,93210,69830,47830,32060,20970,13350,08240,05850,04900,02800,01520,00900,0078
10,06590,25730,37200,39600,36700,31150,24710,20480,18480,13060,08720,06040,0547
20,00200,04060,12400,20970,27530,31150,31770,30730,29850,26130,21400,17400,1641
30,00000,00360,02300,06170,11470,17300,22690,25610,26790,29030,29180,27860,2734
40,00000,00020,00260,01090,02870,05770,09720,12800,14420,19350,23880,26760,2734
50,00000,00000,00020,00120,00430,01150,02500,03840,04660,07740,11720,15430,1641
60,00000,00000,00000,00010,00040,00130,00360,00640,00840,01720,03200,04940,0547
70,00000,00000,00000,00000,00000,00010,00020,00050,00060,00160,00370,00680,0078
800,92270,66340,43050,27250,16780,10010,05760,03900,03190,01680,00840,00460,0039
10,07460,27930,38260,38470,33550,26700,19770,15610,13730,08960,05480,03520,0313
20,00260,05150,14880,23760,29360,31150,29650,27310,25870,20900,15690,11830,1094
30,00010,00540,03310,08390,14680,20760,25410,27310,27860,27870,25680,22730,2188
40,00000,00040,00460,01850,04590,08650,13610,17070,18750,23220,26270,27300,2734
50,00000,00000,00040,00260,00920,02310,04670,06830,08080,12390,17190,20980,2188
60,00000,00000,00000,00020,00110,00380,01000,01710,02170,04130,07030,10080,1094
70,00000,00000,00000,00000,00010,00040,00120,00240,00330,00790,01640,02770,0313
80,00000,00000,00000,00000,00000,00000,00010,00020,00020,00070,00170,00330,0039
900,91350,63020,38740,23160,13420,07510,04040,02600,02070,01010,00460,00230,0020
10,08300,29850,38740,36790,30200,22530,15560,11710,10040,06050,03390,02020,0176
20,00340,06290,17220,25970,30200,30030,26680,23410,21620,16120,11100,07760,0703
30,00010,00770,04460,10690,17620,23360,26680,27310,27160,25080,21190,17390,1641
40,00000,00060,00740,02830,06610,11680,17150,20480,21940,25080,26000,25060,2461
50,00000,00000,00080,00500,01650,03890,07350,10240,11810,16720,21280,24080,2461
60,00000,00000,00010,00060,00280,00870,02100,03410,04240,07430,11600,15420,1641
70,00000,00000,00000,00000,00030,00120,00390,00730,00980,02120,04070,06350,0703
80,00000,00000,00000,00000,00000,00010,00040,00090,00130,00350,00830,01530,0176
90,00000,00000,00000,00000,00000,00000,00000,00010,00010,00030,00080,00160,0020
1000,90440,59870,34870,19690,10740,05630,02820,01730,01350,00600,00250,00120,0010
10,09140,31510,38740,34740,26840,18770,12110,08670,07250,04030,02070,01140,0098
20,00420,07460,19370,27590,30200,28160,23350,19510,17570,12090,07630,04940,0439
30,00010,01050,05740,12980,20130,25030,26680,26010,25220,21500,16650,12670,1172
40,00000,00100,01120,04010,08810,14600,20010,22760,23770,25080,23840,21300,2051
50,00000,00010,00150,00850,02640,05840,10290,13660,15360,20070,23400,24560,2461
60,00000,00000,00010,00120,00550,01620,03680,05690,06890,11150,15960,19660,2051
70,00000,00000,00000,00010,00080,00310,00900,01630,02120,04250,07460,10800,1172
80,00000,00000,00000,00000,00010,00040,00140,00300,00430,01060,02290,03890,0439
90,00000,00000,00000,00000,00000,00000,00010,00030,00050,00160,00420,00830,0098
100,00000,00000,00000,00000,00000,00000,00000,00000,00000,00010,00030,00080,0010