For the simplex tableau given below, enter the current values of the requested variables. \( \left[\begin{array}{rrrrrr}P & x_{1} & x_{2} & s_{1} & s_{2} & \text { Rhs } \\ 0 & 0 & 0 & 1 & 19 & 24 \\ 0 & 1 & 7 & 0 & 7 & 32 \\ \hline 1 & 0 & 12 & 0 & 13 & 140\end{array}\right] \)

To extract the current values of the requested variables from the given simplex tableau, we need to interpret the tableau correctly. The tableau is structured as follows: \[ \begin{array}{|c|c|c|c|c|c|} \hline P & x_{1} & x_{2} & s_{1} & s_{2} & \text{Rhs} \\ \hline 0 & 0 & 0 & 1 & 19 & 24 \\ 0 & 1 & 7 & 0 & 7 & 32 \\ \hline 1 & 0 & 12 & 0 & 13 & 140 \\ \hline \end{array} \] Where: - \( P \) is the objective function value. - \( x_1 \) and \( x_2 \) are the decision variables. - \( s_1 \) and \( s_2 \) are the slack variables. - The last column (Rhs) represents the right-hand side values of the constraints. From the tableau, we can identify the values of the variables: 1. **Basic Variables**: The basic variables are those corresponding to the rows where the leading coefficient (the first non-zero entry in each row) is 1. In this tableau: - The first row corresponds to \( s_1 \) (slack variable) with a value of 24. - The second row corresponds to \( x_1 \) with a value of 32. - The third row corresponds to \( P \) (the objective function) with a value of 140. 2. **Non-basic Variables**: The non-basic variables are those that do not correspond to a leading 1 in their row. In this tableau: - \( x_2 \) and \( s_2 \) are non-basic variables, and their values are 0 (since they do not appear in the basic variable rows). Now, we can summarize the current values of the variables: - \( x_1 = 32 \) - \( x_2 = 0 \) - \( s_1 = 24 \) - \( s_2 = 0 \) - \( P = 140 \) Thus, the current values of the requested variables are: - \( x_1 = 32 \) - \( x_2 = 0 \) - \( s_1 = 24 \) - \( s_2 = 0 \) - \( P = 140 \)