Calculating a different oil spill

After the Deepwater Horizon oil spill, estimating the cost of the cleanup was vital. For my project, we are estimating what the cost would be if the spill lasted a shorter duration, and a different number of people were employed to clean up the spill. This problem can be modeled using a triple integral. The triple integral takes into account the number of barrels of oil spilled, the number of workers employed, and the time frame of the cleanup. The data used in the calculations are derived from the true total cost of the cleanup. This value was roughly $3.2 billion. 200 million gallons of oil were spilled into the Gulf of Mexico. 30,000 people were employed to clean up the spill over a period of 87 days (ABC News; NBC News). 

Suppose there was an oil spill where 150 million barrels of oil were spilled. It took 60 days to clean up the spill, and 25,000 workers were employed for the cleanup. If the cost per barrel per worker per day is the same as in the BP oil spill, what is the total cost of the cleanup?

In this project, we are using the following variables: 

C is the total cost of the clean-up project.

k is a constant, a value derived from the actual oil spill. K is  is the cost per barrel per worker per day, which we calculated as $3.2 billion divided by (200 million barrels * 30,000 workers * 87 days).

x is the number of barrels of oil spilled, which is 150 million.

y is the number of workers, which is 25,000.

t is the time frame of the cleanup in days, which is 60.

After performing the calculations, we find the total cost of the cleanup operation was approximately $1.38 billion, which we estimated using the triple integral. This model shows how the total cost accumulates over time and space. This reflects the complexity of the cleanup operation. Additionally, it shows the importance of accurate calculations and the role of mathematical concepts in responding to such disasters. If the volume of oil being released into the gulf was accurately measured from the start, the cleanup efforts could have been much less costly to the U.S. government.