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Finding the Pivot Row

A pivot row (and the corresponding pivot element) is found by obtaining a ratio by dividing each value in the last column by the corresponding value in the pivot column, excluding the last row (self.objective). The row with the smallest non-negative ratio is the pivot row. If there are no non-negative ratios, the problem doesn't have a solution and we need to abort.

Assignment

Complete the get_pivot_row method. It should return the index of the row to be pivoted and takes the index of the pivot column as input.

Create a last_column list. Fill it with the values from the rightmost column in the tableau, excluding the last row (i.e. self.objective).
Create a pivot_column list. Fill it with the values from the pivot column in the tableau, excluding the last row.
Define a min_ratio variable, initialized to positive infinity; and a min_ratio_idx variable, initialized to -1.
For each index in the last column:
1. Set a ratio variable to positive infinity.
2. If the value in the pivot column at this index is not 0, set the ratio to the value in the last column at this index divided by the value in the pivot column at this index.
3. If the ratio is negative, continue to the next index – this one isn't valid.
4. If the ratio is less than min_ratio, update min_ratio and min_ratio_idx accordingly.
If min_ratio_idx is still -1, raise an Exception with the following message:
```
no non-negative ratios, problem doesn't have a solution
```
Otherwise, return min_ratio_idx; it represents the index of the pivot row.