Problem
Consider the simplex tableau given below. \[ \left[\begin{array}{rrrrrr|r} \mathrm{x}_{1} & \mathrm{x}_{2} & \mathrm{~s}_{1} & \mathrm{~s}_{2} & \mathrm{~s}_{3} & \mathrm{P} & \\ 4 & 1 & 3 & 0 & 0 & 0 & 8 \\ 1 & 0 & 2 & 1 & 0 & 0 & 8 \\ 0 & 0 & 5 & 0 & 1 & 0 & 4 \\ \hline-6 & 0 & -1 & 0 & 0 & 1 & 3 \end{array}\right] \] (A) The pivot element is located in column 1 and row 1 (B) The entering variable is $x_{1}$. (C) The exiting variable is
Solution
Step 1 ：Consider the simplex tableau given below.
Step 2 ：Identify the pivot element. The pivot element is located in column 1 and row 1.
Step 3 ：Determine the entering variable. The entering variable is \(x_{1}\).
Step 4 ：Determine the exiting variable. The exiting variable is \(s_{1}\).
Step 5 ：\(\boxed{\text{Final Answer: The entering variable is } x_{1} \text{ and the exiting variable is } s_{1}}\)
