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cupoosta [38]
3 years ago
5

Se tienen 16 maquinas cuyo rendimiento es del 90% y produce 4800 articulos en 6 dias trabajando 10horas diarias. Si se desea pro

ducir 1200 articulos en 8 dias trabajando 9 horas diarias ¿cuantas maquinas de cuyo rendimiento es del 60% se requieren?
Mathematics
1 answer:
cupoosta [38]3 years ago
5 0

Answer:

5 máquinas.

Step-by-step explanation:

Sabemos que con 16 máquinas, cada una con un rendimiento del 90%, se producen 4800 artículos en 6 días trabajando 10 horas diarias.

Primero extraigamos toda la información útil de esto.

Sea R la velocidad con la que trabaja una máquina con un rendimiento del 100%.

Entonces nuestras máquinas van a trabajar a:

(90%/100%)*R = 0.9*R

16 máquinas juntas trabajaran en total a 16 veces esa cantidad, o:

16*0.9*R

Luego también sabemos que las máquinas trabajan 10 horas al día por 6 días, es decir, trabajan un total de:

6*10h = 60h

60 horas.

Entonces podemos plantear la ecuación:

(16*0.9*R)*60h = 4800 artículos.

Ahora podemos despejar el valor de R.

R = (4800 artículos)/(16*0.9*60 horas) = 5.556 artículos/hora

Ahora:

Se desea producir 1200 artículos.

En 8 días trabajando 9 horas al día, es decir en:

8*9h = 72 horas

Con N máquinas al 60%.

Cada máquina al 60% trabajara con una velocidad de:

0.6*R

N máquinas entonces trabajaran en conjunto a:

N*(0.6*R)

Con la información que se nos da, podemos plantear la ecuación:

N*(0.6*R)*72horas = 1200 artículos.

Queremos resolver esto para N, el número de máquinas, entonces aislamos N

N = (1200 artículos)/((0.6*R)*72horas)

Reemplazando el valor de R, que es 5.556 artículos/hora

N = (1200 artículos)/((0.6*5.556 artículos/hora)*72horas) = 5

Se necesitaran 5 máquinas.

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