mat 271 optimzation project.docx - Daniel 1 Eric Daniel...

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Daniel 1 Eric Daniel March 22, 2018 Mat -271-4130 Optimization Project Introduction: This is a report about the optimization of two cans. A Campbells soup can, and a Bush’s beans can. In this report you see how each can is optimized and which can is best optimized. Can #1: Campbells Cream of Mushroom soup Part 1 -find max volume The radius of this can was found to be 3.5810 cm with a height of 10.5 cm. The computed volume was found to be 423.0073 cm^3 and the computed surface area was found to be 316.8237 cm^2. After taking the surface area equation and putting it in terms of h (h= (316.8237- 2 πr 2 ¿ / 2 πr ¿ / ¿ I was able to take that equation and put into my volume equation V=158.4419- πr 3 and using the first derivate test. I was able to find a maximum new radius for the can which was found to be 4.099a cm and taking that and plugging it in to my surface area equation I found the maximum height to be 8.1994 cm. Using that these to new values I was able to compute that the can’s maximum volume is 432.9695 cm^3. This means the can was 97.9771% optimized. I believe Campbell’s kept optimization in mind when they produced there can. See below are the calculations and a graph of volume vs. radius (The grey dot is the max and the color is the current volume). There will be some error in these calculations because I had to round the numbers.
Daniel 2 Calculations Graph

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