Spartan's Soup Company wants to design a cylindrical can to hold 515 cubic centimeters of soup. Due to lower manufacturing costs, the cans are produced in Iran, where the unit of currency is the rial. The cost of each component of the can depends on the surface area in the finished can. Specifically, the pop-top circular lid costs 299 rials per square centimeter to produce. The side and bottom are machined from one solid piece of steel and cost 216 rials per square centimeter to produce. Determine the radius and height that will minimize the manufacturing cost of the can, and find this minimal cost. (Use the sample problem and solution as a model to follow.) You may use a calculator to help with the arithmetic. Keep at least 4 decimal places during your calculations. Include the following: a well-labeled figure; a clearly defined objective function of one variable with an interval for which that variable is logical, including justification for the construction of the objective function as well as for the bounds of the interval; a calculation of the global extremum with supporting mathematical statements to justify that the optimal result is achieved for the function on the interval within a grammatically correct exposition; a paragraph labeled "Answer" that gives the conclusion in real world terms including units.