3 An initial simplex tableau is shown below.
| \(P\) | \(x\) | \(y\) | \(z\) | \(s\) | \(t\) | RHS |
| 1 | -3 | 1 | 0 | 0 | 0 | 0 |
| 0 | 2 | 0 | 1 | 1 | 0 | 18 |
| 0 | -1 | 2 | 3 | 0 | 1 | 20 |
- Write down the objective for the problem that is represented by this initial tableau.
Variables \(s\) and \(t\) are slack variables.
- Use the final row of the initial tableau to explain what a slack variable is.
- Carry out one iteration of the simplex algorithm and hence:
- give the pivot column used and the value of the pivot element
- write down the value of \(P\) after this iteration
- find the values of \(x , y\) and \(z\) after this iteration
- describe the effect of the iteration geometrically.