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much lower prices at night to encourage customers to use the available power generation capacity and to avoid building new expensive power plants that would be used only a short time during peak periods. Utilities are also willing to purchase power produced during the day from private parties at a high price. Suppose a utility company is selling electric power for $\backslash (\backslash$$ $0\mathrm{.}030/\backslash$mathrm$\{$kWh$\}\backslash )$ at night and is willing to pay $\backslash (\backslash$$ $0\mathrm{.}120/\backslash$mathrm$\{$kWh$\}\backslash )$ for power produced during the day. A pump$-$storage plant has a gross head of $90\mathrm{.}0$ m and can handle a volume flow rate of $\backslash (3\mathrm{.}600\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash )$ in either direction. The irreversible head losses in the system are estimated as $5\mathrm{.}0$ m in either direction at this flow rate. The efficiency of the combined pump$-$motor is $88$ percent and that of the combined turbine$-$generator is $92$ percent. The plant runs in pump mode for $10$ hours each night and runs in turbine mode for $10$ hours each day. It operates $340$ days in a year. How much net revenue $(\backslash$$$)$ does this pump$-$storage plant generate in one year? Take the density of water to be $\backslash (998\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ).$

The net revenue is $\backslash (\backslash$$ $1\backslash )1.$