Formulate the dual for the following linear program

st$.$

${\displaystyle \underset{l=I_k}{\overset{?}{}}}{r}_i{R}_i,A_R,$

${\displaystyle \underset{i=I_0}{\overset{?}{}}}{d}_i{D}_i,A_D,$

$R_i+D_i+S_i,Q_i,$

$D_i+S_i,Q_i,iin{I}_R$

$R_i,D_i,S_i,0,iin{I}_{D0}$

Model Description

$(1)$Maximize total profit

$(2)$Production capacity of regular machines

$(3)$Production capacity of Duplex machines

$(4)$Satisfy demand for cable types that can be made on Duplex or regular machines or outsourced

$(5)$Satisfy demand for cable types that must be made on Duplex machines or outsourced

$(6)$ Non$-$negativity