Consider the simplex tableau given below.
\[
\left[\begin{array}{ccccc|c}
x_{1} & x_{2} & s_{1} & s_{2} & p \\
2 & 1 & 0 & -5 & 0 & 21 \\
2 & 0 & 1 & -5 & 0 & 11 \\
\hline-3 & 0 & 0 & -2 & 1 & 24
\end{array}\right]
\]
(A) Which variables are basic variables?
$\mathrm{x}_{2}, \mathrm{~s}_{1}$, and $\mathrm{P}$
$\mathrm{x}_{2}, \mathrm{~s}_{2}$, and $\mathrm{P}$
$\mathrm{x}_{2}, \mathrm{~s}_{1}$, and $\mathrm{s}_{2}$
$x_{1}, s_{1}$, and $s_{2}$
Answer
Final Answer: The basic variables are \(\boxed{x_{2}, s_{1}, \text{and } p}\).
Step 1 ：Consider the simplex tableau given below.
Step 2 ：\[\left[\begin{array}{ccccc|c} x_{1} & x_{2} & s_{1} & s_{2} & p \\ 2 & 1 & 0 & -5 & 0 & 21 \\ 2 & 0 & 1 & -5 & 0 & 11 \\ \hline-3 & 0 & 0 & -2 & 1 & 24 \end{array}\right]\]
Step 3 ：The basic variables in a simplex tableau are those that have a coefficient of 1 in one row and 0 in all other rows.
Step 4 ：Looking at the given tableau, we can see that the variables \(x_{2}\), \(s_{1}\), and \(p\) are the basic variables because they satisfy this condition.
Step 5 ：Final Answer: The basic variables are \(\boxed{x_{2}, s_{1}, \text{and } p}\).
