Use the simplex method to find the optimal solution to the following problem. Show all of your tableaus. (Note: Keep 4 decimals in your calculations.). In addition, use Gurobi to solve the problem and provide the code and the output of Gurobi.
Maximize x1 - 2x2 + 4x3
subject to
-5x1 - x2 + x3 <= 12
-2x1 - 2x2 + 2x3 <= 14
2x1 + x2 + 2x3 <= 16
x1, x2, x3 >= 0