Given that \(k\) is a constant, display the following linear programming problem in a Simplex tableau.
$$\begin{array} { l l }
\text { Maximise } & P = 6 x + 5 y + 3 z
\text { subject to } & x + 2 y + k z \leqslant 8
& 2 x + 10 y + z \leqslant 17
& x \geqslant 0 , y \geqslant 0 , z \geqslant 0
\end{array}$$
Use the Simplex method to perform one iteration of your tableau for part (a), choosing a value in the \(x\)-column as pivot.
Given that the maximum value of \(P\) has not been achieved after this first iteration, find the range of possible values of \(k\).
In the case where \(k = - 1\), perform one further iteration and interpret your final tableau.