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1

2,5 puntos
Una empresa fabrica dos modelos de patinetes eléctricos (P1 y P2), en tres plantas de producción (A, B y C). Considere las matrices: M=(15010065558570)M=\begin{pmatrix}150&100\\65&55\\85&70\end{pmatrix}, P=(250325)P=\begin{pmatrix}250\\325\end{pmatrix} y H=(111)H=\begin{pmatrix}1&1&1\end{pmatrix}. La matriz MM recoge información sobre el número de unidades de cada modelo fabricado en cada planta de producción. La matriz PP contiene el precio unitario de venta (en euros) de cada modelo de patinete, P1 y P2, respectivamente.
i
Indique la dimensión de la matriz MM. Interprete el significado de su elemento a21a_{21}.0,5 pts
ii
Calcule la matriz H⋅MH\cdot M. Indique su dimensión y explique qué representan sus elementos en el contexto del problema.0,75 pts
iii
Calcule, realizando la operación matricial necesaria, la matriz que refleje, para cada planta de producción, el ingreso obtenido por las ventas de ambos modelos de patinetes. ¿Qué planta es la que obtiene un menor ingreso y cuánto dinero ingresa?1,25 pts

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Tabla de la distribución normal estándar Z∼N(0,1)Z\sim N(0,1)P(Z<k)=12π∫−∞ke−t2/2 dtP(Z\lt k)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{k}e^{-t^2/2}\,dt
Densidad y función de distribución de la normal estándar, con el área bajo la densidad a la izquierda de k sombreada, y los niveles 0,5 y 1 indicados.
kk0123456789
−3,50,00020,00020,00020,00020,00020,00020,00020,00020,00020,0002
−3,40,00030,00030,00030,00030,00030,00030,00030,00030,00030,0002
−3,30,00050,00050,00050,00040,00040,00040,00040,00040,00040,0003
−3,20,00070,00070,00060,00060,00060,00060,00060,00050,00050,0005
−3,10,00100,00090,00090,00090,00080,00080,00080,00080,00070,0007
−3,00,00130,00130,00130,00120,00120,00110,00110,00110,00100,0010
−2,90,00190,00180,00180,00170,00160,00160,00150,00150,00140,0014
−2,80,00260,00250,00240,00230,00230,00220,00210,00210,00200,0019
−2,70,00350,00340,00330,00320,00310,00300,00290,00280,00270,0026
−2,60,00470,00450,00440,00430,00410,00400,00390,00380,00370,0036
−2,50,00620,00600,00590,00570,00550,00540,00520,00510,00490,0048
−2,40,00820,00800,00780,00750,00730,00710,00690,00680,00660,0064
−2,30,01070,01040,01020,00990,00960,00940,00910,00890,00870,0084
−2,20,01390,01360,01320,01290,01250,01220,01190,01160,01130,0110
−2,10,01790,01740,01700,01660,01620,01580,01540,01500,01460,0143
−2,00,02280,02220,02170,02120,02070,02020,01970,01920,01880,0183
−1,90,02870,02810,02740,02680,02620,02560,02500,02440,02390,0233
−1,80,03590,03510,03440,03360,03290,03220,03140,03070,03010,0294
−1,70,04460,04360,04270,04180,04090,04010,03920,03840,03750,0367
−1,60,05480,05370,05260,05160,05050,04950,04850,04750,04650,0455
−1,50,06680,06550,06430,06300,06180,06060,05940,05820,05710,0559
−1,40,08080,07930,07780,07640,07490,07350,07210,07080,06940,0681
−1,30,09680,09510,09340,09180,09010,08850,08690,08530,08380,0823
−1,20,11510,11310,11120,10930,10750,10560,10380,10200,10030,0985
−1,10,13570,13350,13140,12920,12710,12510,12300,12100,11900,1170
−1,00,15870,15620,15390,15150,14920,14690,14460,14230,14010,1379
−0,90,18410,18140,17880,17620,17360,17110,16850,16600,16350,1611
−0,80,21190,20900,20610,20330,20050,19770,19490,19220,18940,1867
−0,70,24200,23890,23580,23270,22960,22660,22360,22060,21770,2148
−0,60,27430,27090,26760,26430,26110,25780,25460,25140,24830,2451
−0,50,30850,30500,30150,29810,29460,29120,28770,28430,28100,2776
−0,40,34460,34090,33720,33360,33000,32640,32280,31920,31560,3121
−0,30,38210,37830,37450,37070,36690,36320,35940,35570,35200,3483
−0,20,42070,41680,41290,40900,40520,40130,39740,39360,38970,3859
−0,10,46020,45620,45220,44830,44430,44040,43640,43250,42860,4247
−0,00,50000,49600,49200,48800,48400,48010,47610,47210,46810,4641
kk0123456789
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
1,20,88490,88690,88880,89070,89250,89440,89620,89800,89970,9015
1,30,90320,90490,90660,90820,90990,91150,91310,91470,91620,9177
1,40,91920,92070,92220,92360,92510,92650,92790,92920,93060,9319
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
3,50,99980,99980,99980,99980,99980,99980,99980,99980,99980,9998