Nanoparticles (3 nm in diameter) of platinum with a total weight of 1 milligram are used in automobile catalytic converters to facilitate oxidation reactions. As Pt is an expensive metal, a method to coat iron nanoparticles with Pt is being explored to reduce the cost of the catalyst metal. If 3 nm diameter Fe particles are being coated with 1 nm of Pt to achieve the same effective surface area with fewer particles and less Pt, calculate the difference in cost and weight of the catalyst. Assume that the cost of Pt is $40/g and that of Fe is $0.005/g. The density of Fe is 7.87 g/cm3 and that of Pt is 21.45 g/cm3.