To insulate high-temperature surfaces it is economical to use two layers of insulation. The first layer is placed next to the hot surface and is suitable for high temperature. It is costly and is usually a relatively poor insulator. The second layer is placed outside the first layer and is cheaper and a good insulator, but does not withstand high temperatures. Essentially, the first layer protects the second layer by providing just enough insulating capability so that the second layer is only exposed to moderate temperatures. Given commercially available insulating materials, design the optimum combination of two such materials to insulate a flat 1000°C surface from ambient air at 20°C. Your goal is to reduce the rate of heat transfer to 0.1% of that without any insulation, to achieve an outer surface temperature that is safe to personnel, and to minimize cost of the insulating package.