you have been hired to build a rectangular box with a square base. the volume of this box is to be 1000 cm3. you want to make this box at minimal cost. each of six faces costs [a] cents per square inch and gluing each of the 12 edges costs [b] cents per (linear) inch of length. find an equation that represents the total cost [c] as a function of x, the length of one side of the base. Suppose a=b=1, find the dimensions of the box of minimal cost. How much would this box cost to construct? Use the graph of c(x) to show that you have a minimum.