Consider the following $($primal$)$ LP model:max $3$x$17$x$2+5$x$3(1$a$)$s$.$t$.2$x$1+3$x$34,(1$b$)4$x$25$x$36,(1$c$)$x$1,$ x$2,$ x$30(1$d$)1.(10$ pt$)$ Let w$1$ and w$2$ be the dual variables associated with constraints $(1$b$)$ and $(1$c$),$respectively. Write down the dual LP model associated with the primal LP model $(1)\mathrm{.}2.(6$ pt$)$ Write down the optimality condition explicitly for checking whether x $=[$x$1$ x$2$ x$3]$and w $=[$w$1$ w$2]$ are optimal solutions to primal LP model $(1)$ and the dual LP model, re$-$spectively, i$.$e$.,$ write down primal feasibility $(2$ pt$),$ dual feasibility $(2$ pt$),$ and complementaryslackness $(2$ pt$)\mathrm{.}3.(4$ pt$)$ Let x $=[$x$1$ x$2$ x$3]$ be an optimal solution to the primal LP model $(1).$ Supposethat we only know that x$1=$ x$2=0$ and constraint $(1$c$)$ is binding at optimality. Given thisinformation, derive the value of w$1$ and w$2\mathrm{.}4.(5$ pt$)$ If the right$-$hand side $6$ in constraint $(1$c$)$ changes to $7,$ then now the constraint$(1$b$)$ is binding at optimality and x$1=$ x$2=0.$ Find the optimal value of this new LP$.$