An efficiency study of the morning shift at a certain factory indicates that an
ID: 2855837 • Letter: A
Question
An efficiency study of the morning shift at a certain factory indicates that an average worker who arrives on the job at 9:00 A.M. will have assembled f(x)=x3+12x2+15x units x hours later. a) Derive a formula for the rate at which the worker will be assembling units after x hours. r(x)=_______. b) At what rate will the worker be assembling units at 10:00 A.M.? The worker will be assembling ______ units per hour. c) How many units will the worker actually assemble between 10:00 A.M. and 11:00 A.M. ? The worker will assemble _________ units.
Explanation / Answer
given f(x)=x3+12x2+15x
a) rate at which the worker will be assembling units after x hours =r(x)=df/dx
r(x)=df/dx=3x2+12*2x+15*1
r(x)=df/dx=3x2+24x+15
b)at 9am , x=0
at 10 am , x=10-9 =1
at 10 am r(1)=3*12+24*1+15
r(1)=36 units per hour
The worker will be assembling 36 units per hour
c)at 11am , t=11-9=2
number units will the worker actually assemble between 10:00 A.M. and 11:00 A.M. =f(2)-f(1)
=[23+12*22+15*2]-[13+12*12+15*1]
=[8+48+30]-[1+12+15]
=70-26
=44
The worker will assemble ___44______ units.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.