A pencil cup with a capacity of 40 in.3 is to be constructed in the shape of a rectangular box with a square base and an open top. If the material for the sides costs 12/in.2 and the material for the base costs 49/in.2, what should the dimensions of the cup be to minimize the construction cost (in )? Round your answer to two decimal places, if necessary, Let x be the length (in in.) of the side of the square base of the open box, and h be the height (in in.) of the box. x = Complete the following parts. (a) Give a function f in the variable x for the quantity to be optimized. (b) f(x)= cents State the domain of this function. (Enter your answer using interval notation.) (c) Give the formula for h in terms of x. h=