Estimate the optimum thickness of insulation for the roof of a house given the following information. The insulation will be installed flat on the attic floor. Overall heat transfer coefficient for the insulation as a function of thickness, U values:

The cost of insulation, including installation, is $120/m³. Capital charges (see Chapter 6) are 20 per cent per year. The cost of fuel, allowing for the efficiency of the heating system is $8/ GJ. The cost of cooling is $5/GJ. Average temperatures for any region of the United States or Canada can be found online at www.weather.com (under the averages tab). Assume the house is heated or cooled to maintain an internal temperature in the range 70 to 80 °F.  

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thickness, mm U. Wm ²K¹ 0 20 25 0.9 50 0.7 100 0.3 150 0.25 200 0.20 250 0.15