Consider a maximization LP in standard form with the usual assumptions. Prove or disprove the following statements; and if applicable, argue which partial statements are true. a. A basic solution x is optimal if and only if its reduced costs are negative. b. Let B be an optimal basis. If one increased the value of a nonbasic variable and adjusts the values of the basic values accordingly (via ???? = ?? ??????), then the objective value function decreases. c. If ?? is an infeasible basic solution with non-positive reduced costs, then ???? ???? for all feasible solutions ??. d. If max{?? ??: ???? = ??, ?? 0} has a finite optimal solution, then the LP max?? ??: ???? = ??, ?? 0 is bounded for all right hand sides ??