A rectangular storage container with an open top is to have a capacity of 107 in. . The length of this base is 3 times the width. What should the dimensions of the container be to minimize the construction cost? Round your answers to two decimal places, if necessary. Let x be the width (in in.) of the base of the container, and h be the height (in in.) of the container. X = in Complete the following parts. (a) Give a function f in the variable x for the quantity to be optimized. f ( x ) = (b) State the domain of this function. (Enter your answer using interval notation.) (c) Give the formula for h in terms of x. h = (d) To determine the optimal value of the function f, we need the critical numbers of --Select-- 4 (e) These critical numbers are as follows. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) X