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The Pivot Operation

The pivot operation's purpose is to move the tableau to the state representing the next better vertex with (in our example) a higher profit value.

Remember, this is what we're simulating:

Assignment

Complete the pivot method. It takes the pivot row and col indexes as inputs, mutates the internal tableau, and returns nothing.

Define a variable pivot_val with the value in self.rows at the location of the pivot row and pivot column – i.e., the value we're pivoting on.
Divide every value in the pivot row by the pivot_val. This is an acceptable operation mathematically: we're dividing both sides of an equation by the same number. The purpose is to make the value at the pivot point 1, by dividing it by itself.
For each row in self.rows:
1. If the row is the pivot row, skip it and go to the next iteration.
2. Define a scalar variable with the value in this row at the pivot column.
3. For each value in this row, subtract from it the product of the scalar and the corresponding value in the pivot row. e.g., self.rows[i][j] -= scalar * self.rows[pivot_row_idx][j].
Define a new scalar with the value in the last row (i.e. self.objective) at the index of the pivot column.
For each value in self.objective, subtract from it the product of the scalar and the corresponding value in the pivot row. e.g. self.objective[i] -= scalar * self.rows[pivot_row_idx][i].