A pencil cup with a capacity of 33 in. is to be constructed in the shape of a right circular cylinder with an open top. If the material for the sides costs 21c/in. and the material for the base costs 38c/in.", what should the radius of the base of the cup be to minimize the construction cost (in +)? Round your answer to two decimal places, if necessary. Let r and h (in in.) be the radius and height of the pencil cup, respectively. r = Lin. Complete the following parts. (a) Give a function fin the variable r for the quantity to be optimized. f(r ) = cents (b ) State the domain of this function. (Enter your answer using interval notation.) (c) Give the formula for h in terms of r. h = (d) To determine the optimal value of the function f, we need the critical numbers of [-Select-- v] . (e) These critical numbers are as follows. (Round your answers to two decimal places, if necessary. Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)