5. The table below shows the cost of transporting one unit of stock from each of four supply points, 1 , 2,3 and 4, to each of three demand points, A, B and C. It also shows the stock held at each supply point and the stock required at each demand point. A minimal cost solution is required.

1. Explain why it is necessary to add a dummy demand point.
2. Add a dummy demand point and appropriate values to Table 1 in the answer book.
3. Use the north-west corner method to obtain a possible solution. After one iteration of the stepping-stone method the table becomes

   	A	B	C	D
   1	15
   2	19	17
   3		3	25
   4	6			14

4. Taking D3 as the entering cell, use the stepping-stone method twice to obtain an improved solution. You must make your method clear by stating your shadow costs, improvement indices, routes, entering cells and exiting cells.
5. Determine whether your solution from (d) is optimal. Justify your answer.