3
Maximise \(\quad P = 2 x - 3 y + 4 z\)
subject to \(\quad x + 2 y + z \leqslant 20\)
\(x - y + 3 z \leqslant 24\)
\(3 x - 2 y + 2 z \leqslant 30\)
and \(\quad x \geqslant 0 , y \geqslant 0 , z \geqslant 0\).

1. Display the linear programming problem in a Simplex tableau.
2. 1. The first pivot to be chosen is from the \(z\)-column. Identify the pivot and explain why this particular value is chosen.
   2. Perform one iteration of the Simplex method.
   3. Perform one further iteration.
3. Interpret your final tableau and state the values of your slack variables.
   [0pt] [3 marks]