Consider the following linear programming Problem P: Minimize X Subject to -2x (1) X + x, 15 (2) +2x, (3) 10 10 *, unconstrained in sign 20 Let the slack of constraint (1) and (2) be xand X respectively, and the surplus of constraint (3) be xg. Answer the following independent questions: 1 Solve the problem graphically: Identify the feasible region by its corner points (coordinates X, and x) and shade it. Find the optimal point on the graph and write the optimal values of the variables and below. 2 Determine the optimal solution, if instead of the minimization the objective was maximization 3 Consider a different objective function: == x;+xz (only for this Question 3) with the same constraints. Find the range of values of the new objective function : in the feasible space of Problem P. Determine the range of values of b, (the rhs of constraint (2), whose current value is 15) that renders Problem P infeasible va Consider decreasing by (the right-hand-side of constraint 3) from its current value of 10. Find the critical value of b, beyond which constraint (3)