Math 311 - Lab 1

Assigned Jan 9
Due Jan 14th Beginning of Class

An oil spill has fouled 200 miles of Paci c shoreline. The oil company responsible has been given 14 days by the Environmental Protection Agency to clean up the shoreline, after which a fine will be levied in the amount of $10,000/day. The local cleanup crew can scrub 5 miles of beach per week, at a cost of $500/day. Additional crews can be brought in to help with the cleanup. Each additional crew costs $18,000 (for transportation and out tting) plus $800/day. Crews are operational 7 days/week.
  1. Find the initial boundaries of the function through these two steps:

    1. Determine the number of days it would take the local crew to clean up the shoreline by itself. What would be the cost to the oil company in this case?

    2. Determine the number of additional crews that need to be brought in to clean up the shoreline within 14 days. What would be the cost to the oil company in this case?

  2. How many additional crews should be brought in to minimize the total cost to the company? How many days would the cleanup cost in this case? What would be the cost to the oil company? Follow the 5-step method, taking care especially with listing all the variables in the problem and any assumptions you are making in the development of the model.

  3. Examine the sensitivity of both the optimal number of crews and the total cost to the rate at which a crew can clean up the shoreline. Include graphs as well as sensitivity values.

  4. Perform sensitivity and robustness analysis by the next two steps:

    1. Examine the sensitivity of both the optimal number of crews and the total cost to the amount of the fi ne levied by the Environmental Protection Agency. Include graphs as well as sensitivity values.

    2. The oil company has led an appeal on the grounds that the amount of the fine is excessive. Assuming that the only purpose of the fine is to motivate the company to clean up the oil spill in a timely manner, do you think the fi ne is excessive? Justify your reasoning based on an appropriate analysis of the model.

  5. The oil spill and the position taken by the oil company has generated a lot of interest in the local newspapers. Some local residents are siding with the company (they are upset that additional crews will be brought in to clean up the oil spill, effectively taking away jobs and employment opportunities from the local population). Others are siding with the Environmental Protection Agency. Wild claims are made by both sides, and there is much confusion about the implication of the fine. You are a cool-headed and mathematically competent journalist who has examined the mathematical model and the results obtained. Write a brief newspaper article (about half a page long) reviewing the case, and interpreting the results and their implications for the general public.