3. The table below shows the cost, in pounds, of transporting one unit of stock from each of four supply points, \(\mathrm { E } , \mathrm { F } , \mathrm { G }\) and H , to three sales points, \(\mathrm { A } , \mathrm { B }\) and C . It also shows the stock held at each supply point and the amount required at each sales point.
A minimum cost solution is required.
| A | B | C | Supply |
| E | 23 | 28 | 22 | 21 |
| F | 26 | 19 | 29 | 32 |
| G | 29 | 24 | 20 | 29 |
| H | 24 | 26 | 19 | 23 |
| Demand | 45 | 19 | 23 | |
- Explain why it is necessary to add a dummy demand point.
- On Table 1 in the answer book, insert appropriate values in the dummy demand column, D.
After finding an initial feasible solution and applying one iteration of the stepping-stone method, the table becomes
| \(A\) | \(B\) | \(C\) | \(D\) |
| \(E\) | 21 | | | |
| \(F\) | 19 | 13 | | |
| \(G\) | | 6 | 23 | |
| \(H\) | 5 | | | 18 |
- Starting with GD as the next entering cell, perform two further iterations of the stepping-stone method to obtain an improved solution. You must make your method clear by showing your routes and stating the
- shadow costs
- improvement indices
- entering and exiting cells
- State the cost of the solution found in (c).
- Determine whether the solution obtained in (c) is optimal, giving a reason for your answer.