Represent the linear programming problem below by an initial Simplex tableau.
$$\begin{array} { l l }
\text { Maximise } & P = 25 x + 14 y - 32 z ,
\text { subject to } & 6 x - 4 y + 3 z \leqslant 24 ,
& 5 x - 3 y + 10 z \leqslant 15 ,
\text { and } & x \geqslant 0 , y \geqslant 0 , z \geqslant 0 .
\end{array}$$
Explain how you know that the first iteration will use a pivot from the \(x\) column. Show the calculations used to find the pivot element.
Perform one iteration of the Simplex algorithm. Show how each row was calculated and write down the values of \(x , y , z\) and \(P\) that result from this iteration.
Explain why the Simplex algorithm cannot be used to find the optimal value of \(P\) for this problem.