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April 19, 2014

Homework Help: Calculus

Posted by Zared on Thursday, November 29, 2012 at 9:50am.

*Optimization problem* I'm okay at some optimization problems, but this one has me stumped.
You work for a company that manufactures circular cylindrical steel drums that can be used to transport various petroleum products. Your assignment is to determine the dimensions (radius and height) of a drum that is to have a volume of 1 cubic meter while minimizing the cost of the drum.
2. The drum has seams around the perimeter of its top and bottom, as well as a vertical seam where edges of the rectangular sheet are joined to form the lateral surface. In addition to the material cost, the cost of welding the seams is $2 per meter. Find the dimensions of the drum that will minimize the cost of production.
3. The cost of shipping each drum from your plant in Birmingham to an oil company in New Orleans depends upon both the surface area of the drum (which determines weight) and the sum of the diameter and the height (which affects how many drums can be transported on one vehicle). The cost is estimated to be $1 per square meter of surface area plus $0.50 per meter of diameter plus height. Find the dimensions of the drum that will minimize the total cost of production and transportation.

I know, its a very lengthy problem, but any help is appreciated

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