Analysis of daily output of a factory during a 8-hour shift shows that

Serotoninl7

Serotoninl7

Answered question

2021-11-13

Analysis of daily output of a factory during a 8-hour shift shows that the hourly number of units y produced after t hours of production is
y=140t+12t2t3, 0t8
a) After how many hours will the hourly number of units be maximized? hr
b) What is the maximum hourly output? unitshr

Answer & Explanation

mylouscrapza

mylouscrapza

Beginner2021-11-14Added 22 answers

Step 1
The number of units proced after t hours of a production is:
y=140t+12t2t3
Where, 0t8
Step 2
First order derivative of y with respect to t is:
dydt=140ddt(t)+12ddt(t2)ddt(t3)
=140(1)+12(2t)3t2[ddx(xn)=nxn1]
=140+t3t2
Second order derivative of y with respect to t is:
d2ydt2=ddt(140)+ddt(t)3ddt(t2)
=0+13(2t)
=16t To maximazed the units, we have to
setdydt=0
140+t3t2=0
3t2t140=0
t=(1)±(1)24(3)(140)2(3)
t=1±1+16806
t=1±416
So, t=1+416=7
And, t=1416=4066.67
Step 3
Since t represents time so it can not be negative.
t=7
At t=7
d2ydt2Bigt=7=16(7)=41<0
Hence, we can say that at

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