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Modeling- Oil Spill

  1. Sep 23, 2013 #1
    An oil spill has fouled 200 miles of shoreline. The oil company responsible has been given 14 days to clean up the shoreline, after which a fine of $$10/day$ will be imposed. The local clean up crew can scrub 5 miles of beach per week at a cost of $500/day. Additional crews can be brought in at a cost of $18 plus $800/day for each crew. How many additional crews should be brought in to minimize the total cost to the company?

    I'm supposed to use these variables:

    n= total number of crews, including the local crew

    n_0=number of crews required to clean up the shoreline in exactly 14 days

    t= number of days to clean up the oil spill

    c= total cost (measured in thousands of dollars)

    t=the amount of the fine (measure in thousands of dollars)

    I'm stuck on this, I am having difficulty putting the pieces together. I'm supposed to find a formula for t in terms of n, t(n).

    How can I relate the number of days to finish the job to the number of crews? How can I find the number of additional crews with my given variables?

    I know that if t>14 or n<n0, then they will have to pay a fine...
     
  2. jcsd
  3. Sep 23, 2013 #2

    tiny-tim

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    Hi SMA_01! :wink:

    Do it step-by-step …

    call the number of crews "n"

    write the equation for the time it will take (as a function of n)

    then write the equation for the cost (as a function of n) …

    show us what you get. :smile:
     
  4. Sep 23, 2013 #3
    tiny-tim,

    Thanks, I got

    t(n)=280/n

    c(t)=500t+(18+800t)(n-1), n>=20
    c(t)=500t+(18+800t)(n-1)+10(t-14)
     
  5. Sep 23, 2013 #4

    tiny-tim

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    Hi SMA_01! :wink:

    That looks good. :smile:

    Now substitute your formula for t(n) into your two formulas for c(n).

    (and don't forget the 280/n has to rounded up to the nearest whole number)
     
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