Consider the following linear programming probleme Minimize Z=2x +32 Subject to 21 54 - - 2x TAIA S3 (2) X 21 and x 20 x2 unconstrained in sign Let the slack of constraint (1) and (2) be x3 and X., respectively, and the surplus of constraint (3) be xs. Answer the following independent questions: 1 (20 points) Solve the problem graphically by hand: Identify the feasible region by its comer points (coordinates x, and x2) and shade it. Find the optimal point(s) on the graph and determine the optimal solution. 2 (5 points) Determine the optimal solution(s), if instead of minimization the objective was maximization 3 (7 points) Write below the basic solution in which X and X; are non-basic variables. Which are the binding (active) constraint(s) at the associated corner point? Z IS (5 points) Determine the range of values of the right hand side of constraint (3), whose current value is that renders the problem infeasible. 5 (5 points) Write an objective function that has multiple optima on the feasible region of probleme (3 points) What is the optimal solution if constraint (3) is removed from the formulation