Question

2. (Core.4) We want to build a cylindrical aluminum can that costs $0.16. Material for the bottom and top cost $0.02 per square inch, and material for the “sides” costs $0.005 per square inch. What is the maximum volume that the cylindrical can may hold? Note: In order to earn a mark of M on this item, you must do all of the following: • Show all the steps of your setup, including a well-labeled diagram, and write at least two sentences to discuss key variables and equations, including a clear statement about what function it is that you are working to optimize and what the domain of that function is. Use calculus in a significant way in the solution, including an argument that explains how calculus demonstrates that your answer actually produces the optimum value that is asked for by the problem statement. That is, how do you know for sure you've found the global max/min? • Write a clear sentence of conclusion for what all of your work ultimately answers

Answer 1

JULY THURSDAY Det Greens ron cheeght hen Area af bottom a top - 9n92 Cost of top 8 bottom= 0.09 x 2092 ----- 0.047182 -Area of sides = 204h -Cost of sides: 0.005 X2A9h - 0.0 Lage -------- - -- Total cost a 0.16 O oy n92 +0.0159 h = 0.16 0 Volime af Cylinder = nath Ne glauf 0:16 –0:04782 _0.01 V oboro.ona 3 --- 0-of -_-oof Valor - 404

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