To start, let us map out the Simplex Tableau as such:
\begin{array} {|c|c|c|c|c|}
\hline BV & z & \text{Variables} & RHS & RT \\
\hline z & 1 & C_{BV}^TB^{-1}N-C_{NBV}^T & C_{BV}^TB^{-1}b & - \\
\hline x_n & 0 & & & \\
\text{or} & 0 & B^{-1}A & & \\
s_n & \vdots & \text{or} & B^{-1}b & \frac{B^{-1}b}{B^{-1}A_j} \\
\text{or} & 0 & B^{-1}A_j & & \\
e_n & 0 & & & \\ \hline
\end{array}
In order to figure out the "Shadow Price" of a Basic Variable (which is really the amount of allowable of change in the original coefficient of a Basic Variable before it changes our current basis) is calculated by the following equation:
$$C^\pi_j=C^T_{BV}B^{-1}Ax_j-Cx_j$$
Where $B^{-1}$ is the entire matrix under the cost-coefficients of the slack variables in the tableau, $A_j$ is the original column coefficients from the constraint of the original model of the chosen variable to calculate, and $C_j$ is the original (non-standardized) cost coefficient in the objective function of the chosen variable.
This will be made more understandable via an Example:
Suppose we want to measure the amount of allowed change of a a basic variable of the following model:
$$\max z = 3x_1+5x_2$$
$$\text{Subject to:}\qquad\qquad\qquad\qquad\qquad\qquad\qquad$$
$$x_1\le4$$
$$2x_2\le12$$
$$3x_1+2x_2\le18$$
$$x_1,x_2\ge0$$
and it has the following optimal final tableau:
\begin{array}{|c|c|}
\hline
BV & z &x_1 & x_2 & s_1 & s_2 & s_3 & RHS \\ \hline
z & 1 & 0 & 0 & 0 & \frac{3}{2} & 1 & 36 \\ \hline
s_1 & 0 & 0 & 0 & 1 & -\frac{1}{3} & -\frac{1}{3} & 2\\
x_2 & 0 & 0 & 1 & 0 & \frac{1}{2} & 0 & 6\\
x_1 & 0 & 1 & 0 & 0 & -\frac{1}{3} & \frac{1}{3} & 2\\
\hline
\end{array}
and we wanted to measure the amount of change if we were to change the original cost of the basic variable $x_2$, then we can measure the allowable amount of change by doing the following to each non-basic variable in the basis:
$$c^\pi_{s_2} = [0, \Delta, 3]B^{-1}A_{s_2}-0$$
$$=[0, \Delta, 3]
\begin{bmatrix}
1 & -\frac{1}{3} & -\frac{1}{3}\\
0 & \frac{1}{2} & 0 \\
0 & -\frac{1}{3} & \frac{1}{3}
\end{bmatrix}
\begin{bmatrix}0\\1\\0\end{bmatrix}$$
$$\Longrightarrow c^\pi_{s_2} = \frac{1}{2}\Delta - 1 \ge 0$$
$$\text{(We don’t want to change the basis)}$$
$$\Longrightarrow\Delta\ge2$$
and,
$$c^\pi_{s_3} = [0, \Delta, 3]B^{-1}A_{s_3}-0$$
$$= [0, \Delta, 3]
\begin{bmatrix}
1 & -\frac{1}{3} & -\frac{1}{3}\\
0 & \frac{1}{2} & 0 \\
0 & -\frac{1}{3} & \frac{1}{3}
\end{bmatrix}
\begin{bmatrix}0\\0\\1\end{bmatrix}$$
$$\Longrightarrow c^\pi_{s_3} = 1$$
$$\text{(Changing $x_2$’s coefficient doesn’t effect $s_3$.)}$$
Thus, the allowable coefficients of $x_2$ that wouldn’t change the basis is $\Delta \ge 2$.
Back to the Problem:
What they may be asking us is the allowable amount of coefficient change of the basic variables $x_1$ and $x_2$, which would be the following for $x_1$:
$$C^\pi_j=[0, \Delta, 4]B^{-1}Ax_j-Cx_j$$
$$=[0, \Delta, 4]
\begin{bmatrix}
1 & -0.714 & -0.571\\
0 & 0.571 & -0.142 \\
0 & -0.142 & 0.285
\end{bmatrix}Ax_j-Cx_j$$
For each non-basic variable in the tableau, and for $x_2$:
$$C^\pi_j=[0, 3, \Delta]B^{-1}Ax_j-Cx_j$$
$$=[0, 3, \Delta]
\begin{bmatrix}
1 & -0.714 & -0.571\\
0 & 0.571 & -0.142 \\
0 & -0.142 & 0.285
\end{bmatrix}Ax_j-Cx_j$$
For each non-basic variable to determine the allowed change for the coefficients of the basic variables.
$$$$
Otherwise, if it isn’t this, then your instructor misspoke and meant the Shadow Price of the slack variables in which is the common convention of the term, which has been answered here.
