Optimization Problems

Tristan

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Dec 3, 2018
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Need some help...
Working on optimization and I don't know how to start a certain problem about worker efficiency.

An efficiency study of the first shift (from 8 A.M. to 5 P.M.) at a certain factory indicates that an average worker who arrives on the job at 8 A.M. will have assembled
Q(t)= -t^3 + 6t^2 +15t transistor radios t hours later. At what time during the shift is the worker performing most efficiently?

Thank you in advance.
 

tkhunny

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Apr 12, 2005
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Need some help...
Working on optimization and I don't know how to start a certain problem about worker efficiency.

An efficiency study of the first shift (from 8 A.M. to 5 P.M.) at a certain factory indicates that an average worker who arrives on the job at 8 A.M. will have assembled
Q(t)= -t^3 + 6t^2 +15t transistor radios t hours later. At what time during the shift is the worker performing most efficiently?

Thank you in advance.
You'll have to define "efficiently". Does that mean "greatest rate"? Could there be a first derivative in your future?
 

Romsek

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Harry_the_cat

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I'm going to take efficiency to mean making the greatest number of radios per unit time. So you're looking for the maximum of \(\displaystyle Q(t)\)

The usual method is to solve \(\displaystyle \dfrac{dQ}{dt} = 0\) for \(\displaystyle t\) and ensuring this is a maximum by checking that \(\displaystyle \dfrac{d^2Q}{dt^2} < 0\)

Can you do that?
I think you need the maximum of Q ' (t).
 
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