Solve each of the following maximization or minimization situations using linear programming. Be sure to include correct mathematical procedures and provide clear and complete explanations and interpretations. In the case that the result is fraction, you will round it to two fraction places. Maximize: z = 3x + 2y Subject to: x + 2y10 3x + y15 x, y 0 (5 points) Maximize: z = 2x + y Subject to: x + y6 x + y1 x, y 0 (5 points) Maximize: z = 4x + 5y Subject to: 2x + y12 x + 3y21 x, y 0 (5 points) Maximize: z = x + 3y Subject to: x + y3 x5 y7 x, y 0 (5 points) Minimize: z = 3x + 4y Subject to: 2x + y8 x + 2y10 x, y 0 (5 points)