# Modeling- Oil Spill

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...

tiny-tim
Homework Helper
Hi SMA_01! 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. • 1 person
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)

tiny-tim
Hi SMA_01! That looks good. 