Optimizing Boom Length for Oil Spill Containment: A Calculus Approach

In summary, to contain oil spills, rectangular booms with a cross-link for stability are used. The minimum total length of boom required to enclose a 100 000 m^2 oil spill using 10-m sections is 250 m by 400 m. However, if 10-m sections are not required, the closest multiples of 10 larger than the length and width would be 250 m and 400 m, respectively. It is unclear if there is a "calculus way" to determine these dimensions.
  • #1
sweet877
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To contain oil spills, rectangular booms that have a cross-link to provide stability are used. The cross-link joins the long sides and is parallel to the short sides. What is the minimum total length of boom required to enclose an oil spill covering 100 000 m^2 of water if it can only be constructed from 10-m sections?

I figured out how to do this if 10-m sections are not required, but cannot figure out what to do if the booms have restrictions. Please advise. Thanks!
 
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  • #2
What length and width do you get if 10-m sections are not required? What are the closest multiples of 10 larger than that?
 
  • #3
250 m and 400 m. But I just got that from common sense. Is there a "calculus way" to do it?
 

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