1. **State the problem:** We have the system of equations: $$2x_1 + 3x_2 + s_1 = 27$$ $$4x_1 + 3x_2 + s_2 = 36$$ and six basic solutions (A) to (F) with values for $x_1$, $x_2$, $s_1$, and $s_2$. 2. **Recall the definition of basic variables:** In a basic solution, the basic variables are those that are not zero and correspond to the columns forming the basis in the simplex method. Non-basic variables are set to zero. 3. **Analyze solution (A):** $$(A): x_1=0, x_2=0, s_1=27, s_2=36$$ Here, $x_1$ and $x_2$ are zero, while $s_1$ and $s_2$ are nonzero. 4. **Conclusion:** The basic variables in solution (A) are $s_1$ and $s_2$ because they have nonzero values and the other variables are zero. **Final answer:** The basic variables in solution (A) are $s_1$ and $s_2$.