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Modeling- Oil Spill

  • Thread starter SMA_01
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  • #1
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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...
 

Answers and Replies

  • #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:
 
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  • #3
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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)
 
  • #4
tiny-tim
Science Advisor
Homework Helper
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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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