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Optimizing Oil Spill Cleanup: Minimizing Costs with Additional Crews
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[QUOTE="SMA_01, post: 4512578, member: 325092"] 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 into 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... [/QUOTE]
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Optimizing Oil Spill Cleanup: Minimizing Costs with Additional Crews
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