$1.($lecture $4)($Problem $4\mathrm{.}4-8)$ Simplex method for Maximize Z $=$ x$1+$ x$2+2$x$32.($lecture $4)$ Simplex method for $(1$c$)$ in the first homework assignment$\mathrm{.}3.($lecture $5)$ We do not cover the simplex method to solve the dual problem on slide $5-2,$ so we will use Gurobi to solve it$.$ Please use m$.$Params.method $=0$ in theprogram parameter for the primal simplex method.$($a$)$ What is the optimal solution of y$?($b$)$ What is the optimal objective value?$($c$)$ What is the duality gap?$4.($lecture $5)$ Problem $4\mathrm{.}9\mathrm{.}2$ Reconsider the model in Prob. $4\mathrm{.}1\mathrm{.}5($Problem $4\mathrm{.}7-2$ in the $10$th edition$)5.($lecture $5)$ Problem $7\mathrm{.}3-6$ David, LaDeana, and Lydia $($Problem $7\mathrm{.}3-8$ in the $10$th edition. Please skip problems $($e$,$ f$,$ h$,$ m$,$ n$))$