3. (a) (25 points) Solve the following linear programming problem using the simplex method. Show that the optimal value is 39.9, and write down an optimal solution. Maximize 13.01 + 15x2 + 12x3 Subject to 2.61 +222 + 33 0 AMA 505 Midterm (b) (5 points) Using part (a), or otherwise, solve the following linear programming problem. Write down the optimal value and an optimal solution. AMA 505 Midterm (b) (5 points) Using part (a), or otherwise, solve the following linear programming problem. Write down the optimal value and an optimal solution. Minimize 241 + 5y2 Subject to y1 + 742 >12, 2y1 + 2y2 > 13, 2yi - 6y2 > 15, 41, 42 > 0. (c) (5 points) Using part (a), or otherwise, solve the following linear programming problem. Write down the optimal value and an optimal solution. Maximize 13.01 + 15x2 + 12.13 Subject to 2.01 +212 +13 0