4. A linear programming problem in \(x , y\) and \(z\) is to be solved using the big-M method. The initial tableau is shown below.
| b.v. | \(x\) | \(y\) | \(z\) | \(S _ { 1 }\) | \(s _ { 2 }\) | \(S _ { 3 }\) | \(a _ { 1 }\) | \(a _ { 2 }\) | Value |
| \(\mathrm { S } _ { 1 }\) | 2 | 3 | 4 | 1 | 0 | 0 | 0 | 0 | 13 |
| \(a _ { 1 }\) | 1 | -2 | 2 | 0 | -1 | 0 | 1 | 0 | 8 |
| \(a _ { 2 }\) | 3 | 0 | -4 | 0 | 0 | -1 | 0 | 1 | 12 |
| P | 2-4M | \(- 3 + 2 M\) | \(- 1 + 2 M\) | 0 | M | M | 0 | 0 | \(- 20 M\) |
- Using the information in the above tableau, formulate the linear programming problem. You should
- list each of the constraints as an inequality
- state the two possible objectives
- Obtain the most efficient pivot for a first iteration of the big-M method. You must give reasons for your answer.
\section*{Please turn over for Question 5}