Problem $2(75$ points$)$ Consider the following linear programming problem $\backslash ($ P $\backslash ).$ Let the surplus of constraint $(1)$ and $(2)$ be $\backslash ($ x$\_\{3\}\backslash )$ and $\backslash ($ x$\_\{4\}\backslash ),$ respectively, and the slack of constraint $(3)$ be $\backslash ($ x$\_\{5\}\backslash ).$ Answer the following independent questions: $1$ Solve the problem graphically: Identify the feasible region by its corner points $($coordinates $\backslash ($ x$\_\{1\}\backslash )$ and $\backslash ($ x$\_\{2\}\backslash ))$ and shade it$.$ Find the optimal point on the graph and write the optimal values of the variables and $\backslash ($ z $\backslash ),$ below. $2$ Determine the optimal solution, if instead of minimization the objective was maximization. $3$ Write an objective function that has multiple optima on the feasible region of problem $\backslash (\backslash$mathcal$\{$P$\}\backslash ).4$ Determine a right hand side value of constraint $(3)$ that renders the problem infeasible. Note that there are many values with that property. $5$ What is the optimal solution if constraint $(3)$ is removed from the formulation? $6$ Construct the initial basic solution by adding artificial variables and making the necessary variable transformations so that you can apply the Big M method to Problem P$.$ Set up Big M method iteration $(0)$ tableau. Indicate the entering and leaving variable and perform a single iteration. Write the resulting basic solution of iteration $(1)$ and indicate whether it is feasible or infeasible to Problem $\backslash ($ P $\backslash ).$ Indicate on the graph the point this basic solution corresponds to and the constraints $($if any$)$ that are violated.