$(30$ pts$)$ A pump$-$storage plant uses a turbine to generate hydropower during the day, letting water from the upper reservoir flow through the turbine into the lower reservoir as sketched. The plant then pumps water back up to the upper reservoir during the night. In a typical pump$-$storage plant, the same turbomachine is used as both the pump and the turbine and is called a pump$-$turbine. The plant is profitable because the demand for electric power is much higher during the day than it is at night, and utility companies sell power at 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 $$\frac{0\mathrm{.}035}{k}Wh$ at night and is willing to pay $$\frac{0\mathrm{.}140}{k}Wh$ 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 $9\mathrm{.}51\frac{m^3}{s}$ in either direction. The irreversible head losses in the system are estimated as $8\mathrm{.}55$ m in either direction at this flow rate. The efficiency of the combined pump$-$motor is $88\%$ and that of the combined turbine$-$generator is $92\%.$ The plant runs in pump mode for $10$ hours each night and runs in turbine mode for $10$ hours each day. It operates $349$ days in a year. How much net revenue $($$$)$ does this pump$-$storage plant generate in one year? For consistency use $1000k\frac{g}{m^3}$ as the density of water.