# solution

Consider the following linear programming problem : Minimize z=Xi – 2×2, subject to XI – X2 <1 (1) X1 + x2 < 2 -X <1 (3) and xi unconstrained in sign X2 unconstrained in sign Let the slack of constraint (1) be x3, the slack of constraint (2) be x4, and the slack of constraint (3) be X5. Answer the following independent questions (Note: Do NOT use Simplex to solve this Linear Programming problem). 1 (20 points) Solve the problem graphically (manually by hand): Identify the feasible region by its corner points (coordinates xi and x2) and shade the optimal point on the graph. 2 (5 points) What is the optimal solution, if instead of minimiz maximization? ion the objective was 3 (7 points) Write below the basic solution in which x3 and x4 are non-basic variables. X2= Which are the binding ctive) constraints at the associated corner point? X/= X5 4 (5 points) Determine the range of values of the right-hand side of constraint (1), whose current value is 1, which renders the problem infeasible. 5 ective function that has multiple optima on the feasible region of 6 PESO Ace when (3 points) What is the optimal solution if constraint (1) is removed from the formulation?