Consider the following primal problem

Min x

$2$

$1+$ x

$2$

$24$x$14$x$2$

s$.$t$.$ x

$2$

$1<=$ x$2$

x$1+$ x$2<=2$

i$)$ Find the dual of the above. $(2$ marks$)$

ii$)$ Will dual and primal have same optimal function value? Justify.