$2\mathrm{.}62$ Shown in Fig. P$2\mathrm{.}62$ is a cogeneration power plant operating in a thermodynamic cycle at steady state. The plant provides electricity to a community at a rate of $80$ MW $.$ The energy discharged from the power plant by heat transfer is denoted on the figure by $Q_{\text{o}\text{u}\text{t}}^{}.$ Of this, $70$ MW is provided to the community for water heating and the remainder is discarded to the environment without use. The electricity is valued at $$0\mathrm{.}08$ per $kW*h.$ If the cycle thermal efficiency is $40\%,$ determine the $($a$)$ rate energy is added by heat transfer, $Q_{in}^{},$ in MW$,($b$)$ rate energy is discarded to the environment, in MW$,$ and $($c$)$ value of the electricity generated, in $ per year.