Display the following linear programming problem in a Simplex tableau.
$$\begin{array} { l r }
\text { Maximise } & P = 2 x + 3 y + 4 z
\text { subject to } & x + y + 2 z \leqslant 20
& 3 x + 2 y + z \leqslant 30
& 2 x + 3 y + z \leqslant 40
\text { and } & x \geqslant 0 , y \geqslant 0 , z \geqslant 0
\end{array}$$
The first pivot to be chosen is from the \(z\)-column. Identify the pivot and explain why this particular value is chosen.
Perform one iteration of the Simplex method.
Perform one further iteration.
Interpret your final tableau and state the values of your slack variables.