Display the following linear programming problem in a Simplex tableau.
Maximise \(\quad P = x - 2 y + 3 z\)
subject to
$$\begin{array} { r }
x + y + z \leqslant 16
x - 2 y + 2 z \leqslant 17
2 x - y + 2 z \leqslant 19
\end{array}$$
and \(x \geqslant 0 , y \geqslant 0 , z \geqslant 0\).
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 the tableau that you obtained in part (c)(i) and state the values of your slack variables.