Final answer:
The Simplex algorithm is used to solve linear programming problems, but it can result in cycling. To solve the problem using the modified lexicographical pivoting rule 2, you need to apply the Simplex algorithm steps.
Step-by-step explanation:
The Simplex algorithm is used to solve linear programming problems. However, in some cases, the Simplex algorithm can result in cycling. Cycling occurs when the algorithm keeps revisiting the same solution without making progress towards the optimal solution.
In order to solve the problem using the modified lexicographical pivoting rule 2, we need to apply the steps of the Simplex algorithm. However, since the specific problem is not provided in the question, it is not possible to show all the work. To solve the problem, you would need to follow the pivot steps, update the tableau, and continue until an optimal solution is reached.