SOLUTION: Chicago Public Water and Sewer Department collects s cubic meter of sewerage annually. The sewerage is collected and treated in a cylindrical container sunken into the ground with

Question 1156037: Chicago Public Water and Sewer Department collects s cubic meter of sewerage annually. The sewerage is collected and treated in a cylindrical container sunken into the ground with a radius of r meters and a depth of h meters which lasts for one year before the metallic sides must be replaced. The top and bottom of the container are made of specially formulated materials which are never replaced. The metallic sides of the container cost m dollars per square meter to make. When full, the container is treated to neutralize the sewerage, then emptied, and the interior surfaces including the top and bottom are documented at a cost of d dollars per square meter.
a) What is the parameterized expression for yearly container plus documentation cost as a function of r?
b) As a function of r, what dimensions and cost minimize the expression in (a)?
c) If the total annual sewerage is 100,000 cubic meters, the depth is fixed at 50 meters, the cost of making the sides is $500 per square meter, and the cost of documentation is $25 per square meter, what radius minimizes the cost? What is this minimum cost?

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