1. **State the problem:** We need to write the equation associated with the inequality $$7x_1 + 6x_2 \leq 13$$ by introducing a slack variable $$s_1$$. 2. **Explain slack variables:** Slack variables are added to convert inequalities into equalities in linear programming. For a constraint of the form $$ax + by \leq c$$, we add a slack variable $$s \geq 0$$ such that $$ax + by + s = c$$. 3. **Apply the formula:** For the inequality $$7x_1 + 6x_2 \leq 13$$, add slack variable $$s_1 \geq 0$$: $$7x_1 + 6x_2 + s_1 = 13$$ 4. **Interpretation:** This equation means the sum of $$7x_1$$, $$6x_2$$, and the slack $$s_1$$ exactly equals 13, where $$s_1$$ represents unused resources or capacity. **Final answer:** $$7x_1 + 6x_2 + s_1 = 13$$