1. **State the problem:** We need to find the pivot column in the simplex tableau for maximizing $P = 35x_1 + x_2$. 2. **Recall the simplex method rule for pivot column:** The pivot column is the column with the most negative coefficient in the bottom row (objective function row) of the tableau. 3. **Look at the bottom row coefficients:** $$-35 \quad -1 \quad 0 \quad 0$$ 4. **Identify the most negative coefficient:** The most negative value is $-35$ in the $x_1$ column. 5. **Conclusion:** The pivot column is the $x_1$ column.