Problem A

What is the cheapest soup can that will hold 75in3 (cubic inches) of soup? Assume the can is cylindrical in shape and that the total cost of a can is proportional to the amount of material (tin) measured as area (in other words, don’t worry about the thickness of the tin). Be sure to provide both the diameter (or radius) and height of the can and sketch what this cheapest can looks like!

Problem B

Repeat the above problem but for the case where, for whatever reason, the cost of manufacturingthe two lids of the can is three times higher than manufacturing the sidewall. Give your answer in the same form as above, including the sketch.