Consider the following optimization model. 10 x Maximize Z= -100 x + 50 x s.t. 6x + 6 x 0 (Non-negativity constraints) a. Give an upper bound on the number of corner points of the problem. Find those points and indicate whether each point is feasible, infeasible, or inconsistent. b. Determine and draw the feasible region for this model. Make sure that you clearly label all the constraints and points in your drawing. c. Solve the problem and find the optimal solution(s). What is your conclusion? Explain your reasoning. d. Draw the objective function contour where it is equal to optimal objective value. Consider the following optimization model. Minimize Z= 2 x + x s.t. -5x + 5x 0 (Non-negativity constraints) Determine and draw the feasible region for this model. Make sure that you clearly label all the constraints and corner points in your drawing. b. Solve the problem and find the optimal solution(s). c. Draw the objective function contour where it is equal to optimal objective value. d. Suppose that it is a maximization problem with the same objective function and constraints. Solve the problem and find the optimal solution(s). What is your conclusion for part d? Explain your reasoning. a. e