$4-4.$ Write the dual for each of the following primal problems:$($a$)$ Maximize z $=66$x$1-22$x$2$subject to$-$x$1+$ x$2$ smaller than or equal $-22$x$1+3$x$2$ smaller than or equal $5$x$1,$ x$2$ greater than or equal $0($b$)$ Minimize z $=6$x$1+3$x$2$subject to$6$x$1-3$x$2+$ x$3$ greater than or equal $253$x$1+4$x$2+$ x$3$ greater than or equal $55$x$1,$ x$2,$ x$3$ greater than or equal $0($c$)$ Maximize z $=$ x$1+$ x$2$subject to$2$x$1+$ x$2=53$x$1-$ x$2=6$x$1,$ x$2$ unrestricted$4-4.$ Write the dual for each of the following primal problems:$($a$)$ Maximize z $=66$x$1-22$x$2$subject to$-$x$1+$ x$2$ smaller than or equal $-22$x$1+3$x$2$ smaller than or equal $5$x$1,$ x$2$ greater than or equal $0($b$)$ Minimize z $=6$x$1+3$x$2$subject to$6$x$1-3$x$2+$ x$3$ greater than or equal $253$x$1+4$x$2+$ x$3$ greater than or equal $55$x$1,$ x$2,$ x$3$ greater than or equal $0($c$)$ Maximize z $=$ x$1+$ x$2$subject to$2$x$1+$ x$2=53$x$1-$ x$2=6$x$1,$ x$2$ unrestricted