- A linear programming problem is defined as follows:
$$\begin{array} { l l }
\text { Maximise } & P = 3 x + 3 y + 4 z \\
\text { subject to } & x + 2 y + z \leq 30 \\
& 5 x + y + 3 z \leq 60 \\
\text { and } & x \geq 0 , y \geq 0 , z \geq 0 .
\end{array}$$
- Display the problem in a Simplex Tableau.
- Starting with a pivot chosen from the \(z\)-column, perform one iteration of your tableau.
- Write down the resulting values of \(x , y , z\) and \(P\) and state with a reason whether or not these values give an optimal solution.