1. A linear programming problem is defined as follows:

$$\begin{array} { l l } \text { Maximise } & P = 3 x + 3 y + 4 z
\text { subject to } & x + 2 y + z \leq 30
& 5 x + y + 3 z \leq 60
\text { and } & x \geq 0 , y \geq 0 , z \geq 0 . \end{array}$$

1. Display the problem in a Simplex Tableau.
2. Starting with a pivot chosen from the \(z\)-column, perform one iteration of your tableau.
3. 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.