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 $n<n_0$, then they will have to pay a fine...