Determine the optimum economic thickness of insulation

Under the following conditions, determine the optimum economic thickness of insulation for a 1-in. standard pipe carrying saturated steam at 100 psig. The line is in use continuously. The covering specified is light carbonate magnesia, which is marketed in whole-number thicknesses only (i.e., 1 in., 2 in., 3 in., etc.). The cost of the installed insulation may be approximated as $20 per cubic foot of insulation. Annual fixed charges are 20 percent of the initial investment, and the heat of the steam is valued at $1.50 per 1 million Btu. The temperature of the surroundings may be assumed to