For a transportation problem, let \(c_{ij}\) denote the unit cost of the cell \((i, j)\). The known unit costs are shown below (a dash marks a cell whose cost is not given).
| j = 1 | j = 2 | j = 3 |
|---|
| i = 1 | 10 | 12 | 19 |
| i = 2 | 11 | 13 | - |
| i = 3 | - | - | - |
Let \(\alpha_i\) and \(\beta_j\), \(i, j = 1, 2, 3\), be the simplex multipliers associated with a basis corresponding to this unit cost table, so that \(\alpha_1 = x\), \(\alpha_2 = x + 1\), \(\beta_1 = y\) and \(\beta_2 = y + 2\). The relative cost coefficient \(d_{ij}\) is the difference between the current solution and the new improved solution.
If \(x = 4\), \(c_{13} = 19\) and \(\beta_3 = y + 5\), then which one of the following is TRUE?