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B2

3 puntos
Apartado B

Elige uno de los siguientes problemas y resuélvelo, justificando las respuestas:

Una panadería fabrica cajas de mantecados y de perrunillas. Para su elaboración cuenta diariamente con 40 kg40\,\text{kg} de harina y 50 kg50\,\text{kg} de azúcar, necesitando 1 kg1\,\text{kg} de harina y 2 kg2\,\text{kg} de azúcar para cada caja de mantecados, con un beneficio de 10 €10\,\text{€}. Por otra parte, para fabricar una caja de perrunillas, que le aporta un beneficio de 15 €15\,\text{€}, utiliza 2 kg2\,\text{kg} de harina y 1 kg1\,\text{kg} de azúcar. Sabiendo que, por cuestiones de abastecimiento, el número de cajas de perrunillas debe ser, como mucho, el doble que el de cajas de mantecados, calcula el número de cajas de cada producto que debe fabricar diariamente para obtener unos beneficios máximos y el valor de esos beneficios.

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ANEXO TABLA DISTRIBUCIÓN NORMAL Tabla de distribución normal N(0,1)N(0, 1) F(z)=P(Z≤z)F(z) = P(Z \leq z)
Área acumulada de la distribución normal tipificada Campana simétrica respecto a cero. El área F(z) se extiende desde menos infinito hasta z, situado a la derecha de cero. F(z) 0 z −∞ +∞
zz0,000,010,02
0,00,50000,50400,5080
0,10,53980,54380,5478
0,20,57930,58320,5871
0,30,61790,62170,6255
0,40,65540,65910,6628
0,50,69150,69500,6985
0,60,72570,72910,7324
0,70,75800,76110,7642
0,80,78810,79100,7939
0,90,81590,81860,8212
1,00,84130,84380,8461
1,10,86430,86650,8686
1,20,88490,88690,8888
1,30,90320,90490,9066
1,40,91920,92070,9222
1,50,93320,93450,9357
1,60,94520,94630,9474
1,70,95540,95640,9573
1,80,96410,96490,9656
1,90,97130,97190,9726
2,00,97720,97780,9783
2,10,98210,98260,9830
2,20,98610,98640,9868
2,30,98930,98960,9898
2,40,99180,99200,9922
2,50,99380,99400,9941
2,60,99530,99550,9956
2,70,99650,99660,9967
2,80,99740,99750,9976
2,90,99810,99820,9982
3,00,99870,99870,9987
3,10,99900,99910,9991
3,20,99930,99930,9994
3,30,99950,99950,9995
3,40,99970,99970,9997
3,50,99980,99980,9998
3,60,99980,99980,9999
3,70,99990,99990,9999
3,80,99990,99990,9999
3,91,00001,00001,0000
zz0,030,040,05
0,00,51200,51600,5199
0,10,55170,55570,5596
0,20,59100,59480,5987
0,30,62930,63310,6368
0,40,66640,67000,6736
0,50,70190,70540,7088
0,60,73570,73890,7422
0,70,76730,77040,7734
0,80,79670,79950,8023
0,90,82380,82640,8289
1,00,84850,85080,8531
1,10,87080,87290,8749
1,20,89070,89250,8944
1,30,90820,90990,9115
1,40,92360,92510,9265
1,50,93700,93820,9394
1,60,94840,94950,9505
1,70,95820,95910,9599
1,80,96640,96710,9678
1,90,97320,97380,9744
2,00,97880,97930,9798
2,10,98340,98380,9842
2,20,98710,98750,9878
2,30,99010,99040,9906
2,40,99250,99270,9929
2,50,99430,99450,9946
2,60,99570,99590,9960
2,70,99680,99690,9970
2,80,99770,99770,9978
2,90,99830,99840,9984
3,00,99880,99880,9989
3,10,99910,99920,9992
3,20,99940,99940,9994
3,30,99960,99960,9996
3,40,99970,99970,9997
3,50,99980,99980,9998
3,60,99990,99990,9999
3,70,99990,99990,9999
3,80,99990,99990,9999
3,91,00001,00001,0000
zz0,060,070,08
0,00,52390,52790,5319
0,10,56360,56750,5714
0,20,60260,60640,6103
0,30,64060,64430,6480
0,40,67720,68080,6844
0,50,71230,71570,7190
0,60,74540,74860,7517
0,70,77640,77940,7823
0,80,80510,80780,8106
0,90,83150,83400,8365
1,00,85540,85770,8599
1,10,87700,87900,8810
1,20,89620,89800,8997
1,30,91310,91470,9162
1,40,92790,92920,9306
1,50,94060,94180,9429
1,60,95150,95250,9535
1,70,96080,96160,9625
1,80,96860,96930,9699
1,90,97500,97560,9761
2,00,98030,98080,9812
2,10,98460,98500,9854
2,20,98810,98840,9887
2,30,99090,99110,9913
2,40,99310,99320,9934
2,50,99480,99490,9951
2,60,99610,99620,9963
2,70,99710,99720,9973
2,80,99790,99790,9980
2,90,99850,99850,9986
3,00,99890,99890,9990
3,10,99920,99920,9993
3,20,99940,99950,9995
3,30,99960,99960,9996
3,40,99970,99970,9997
3,50,99980,99980,9998
3,60,99990,99990,9999
3,70,99990,99990,9999
3,80,99990,99990,9999
3,91,00001,00001,0000
zz0,09
0,00,5359
0,10,5753
0,20,6141
0,30,6517
0,40,6879
0,50,7224
0,60,7549
0,70,7852
0,80,8133
0,90,8389
1,00,8621
1,10,8830
1,20,9015
1,30,9177
1,40,9319
1,50,9441
1,60,9545
1,70,9633
1,80,9706
1,90,9767
2,00,9817
2,10,9857
2,20,9890
2,30,9916
2,40,9936
2,50,9952
2,60,9964
2,70,9974
2,80,9981
2,90,9986
3,00,9990
3,10,9993
3,20,9995
3,30,9997
3,40,9998
3,50,9998
3,60,9999
3,70,9999
3,80,9999
3,91,0000