$(13$ points$)$ Assume Generator $1$ and $2$ from Problem $1$ are connected to Buses $1$ and $2,$ respectively, in the

following diagram, where the network data are given in the table. Formulate the DC optimal power flow

problem by specifying the objective function, decision variables, and all of the constraints. You do not need

to put the objective function or constraints into any particular standard form and you do not need to solve

the optimization problem. Assume Bus $1$ is the slack bus and $x_{ij}=b_{ij}^{-1}($since $r_{ij}$ is relatively small$).$ Also,

assume each generator's minimum output is $0MW.$Assume Generator $1$ and $2$ from Problem $1$ are connected to Buses $1$ and $2,$ respectively, in the

following diagram, where the network data are given in the table. Formulate the DC optimal power flow

problem by specifying the objective function, decision variables, and all of the constraints. You do not need

to put the objective function or constraints into any particular standard form and you do not need to solve

the optimization problem. Assume Bus $1$ is the slack bus and xij $=$ b$1$

ij $($since rij is relatively small$).$ Also,

assume each generator$$s minimum output is $0$ MW