System Design 403 CH.docx - Design a can to hold at least 400 ml of liquid The cans will be produced in the billions so it is desirable to minimize

System Design 403 CH.docx - Design a can to hold at least...

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Design a can to hold at least 400 ml of liquid. The cans will be produced in the billions, so it is desirable to minimize their manufacturing costs Since cost can be directly related to the surface area of the sheet metal used, it is reasonable to minimize the amount of sheet metal required Fabrication, handling, aesthetics, and shipping considerations impose the following restrictions on the size of the can: The diameter should be no more than 8 cm and no less than 3.5 cm, whereas the height should be no more than 18 cm and no less than 8 cm Variables that needs to be found : D and H. Restrictions: 3.5 ≤ D ≤ 8 cm; 8cm ≤ H ≤ 18cm
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Unformatted text preview: Optimization Criterion: Surface area of the cylinder and two ends must be minimized Surface Area S = 2 πrH + 2 ( π 4 D 2 ) Constraints formula: The can could hold 400 ml of fluid: π r 2 H ≥ 400 Volumeof Cylinder V = π r 2 H 400 = πr 2 H 400 π r 2 = H S = 2 πr 400 π r 2 + 2 π r 2 S = 400 ∗ 2 r + 2 π r 2 Deriving S ' S ' = 800 r − 2 + 4 πr Solving for r = 800 r − 2 − 4 πr r 3 = 800 4 π Therefore: r = 3.99 cm H = 400 3.99 2 ∗ π H = 8 cm 3.5 ≤ D ≤ 8 cm; 8cm ≤ H ≤ 18cm Diameter Dimension 3.5 ≤ 7.98 ≤ 8 cm Height Dimension 8cm ≤ 8cm ≤ 18cm...
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