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Math · Calculus
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In class, we found the dimensions of a right circular cylinder (a can) that has a volume of using the minimum possible material. This assignment changes that problem slightly by seeking the minimum cost for a right circular cylinder whose volume is where the cost of materials for the bottom, top, and side are different. Suppose the materials for the bottom of your cylinder cost 0.5 cents per square centimeter the materials for the top cost 0.4 cents per square centimeter; and the materials for the side cost 0.2 cents for square centimeter: 1. (Three points.) Write a function for the total cost of the cylinder in terms of its radius O and its height O 2. (Three points.) Write an equation expressing the volume in terms of the radius and height. Solve your equation for either or and substitute the result into your cost function 3. (Three points.) Use your calculator to graph the cost function from Problem 2 and find where its minimum occurs. Make a rough sketch of the graph and give the coordinates of the minimum 4. (Three points.) The -coordinate of the minimum is the value for or (whichever you ended up with in your cost function in Problem 2) that produces the cylinder of minimum cost. Now use your work in Problem 2 to find the other, and state the radius and height of the cylinder of minimum cost. Round both values to the nearest tenth of a centimeter
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