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Thread: Optimization Problems

  1. #1

    Optimization Problems

    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.

  2. #2
    Elite Member
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    Quote Originally Posted by Tristan View Post
    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?
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

  3. #3
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    deleted
    Last edited by Romsek; 12-04-2018 at 05:42 AM.

  4. #4
    Quote Originally Posted by Romsek View Post
    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 [tex]Q(t)[/tex]

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

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

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