Problem $4.(20$ points$)$ An electric utility must determine which generators to start up at the beginning of each day. They have three generators with capacities, operating cost, and start$-$up costs shown in the following table. A day is divided into two periods, and each generator may be started at the beginning of each period. A generator started in period $1$ may be used in period $2$ without incurring an additional start$-$up cost$.$ All generators are turned off at the end of the day. Demand for power is $2500$ megawatts $($MW$)$ in period $1$ and $3500$ MW in period $2.$ Formulate this problem so as to minimize daily operating cost. Define the binary and continuous $($if any$)$ variables carefully. $\backslash$begin$\{$tabular$\}\{$cccc$\}\backslash$hline Generator & $\backslash$begin$\{$tabular$\}\{$c$\}$ Fixed start$-$up $\backslash \backslash$ cost $(\backslash$$$)\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$ Cost per period $\backslash \backslash$ per megawatt $\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$ Generator capacity in $\backslash \backslash$ each period $($MW$)\backslash$end$\{$tabular$\}\backslash \backslash \backslash$hline $1$ & $2800$ & $5$ & $1900\backslash \backslash 2$ & $2000$ & $3$ & $1700\backslash \backslash 3$ & $1900$ & $8$ & $2900\backslash \backslash \backslash$hline $\backslash$end$\{$tabular$\}$