A solar system is to be installed in Phoenix, Arizona. The estimated amounts of energy from the system as a function of collector area are shown in the following tabulation. If the solar system costs \(\$ 195 / \mathrm{m}^{2}\) and is to be paid off over 25 years at \(10 \%\) interest, prepare the total cost curve and specify the cost optimal system. Assume that the backup fuel is fuel oil at \(\$ 7 / G J\) and that the fuel price is inflating at \(8 \% /\) year. The total energy demand for which the solar system is constructed is estimated to be \(1000 \mathrm{GJ} /\) year.

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Collector Energy Area (m) Delivered (GJ) 100 336 150 444 200 531 250 612 300 673 400 791 500 856 600 915