D2 June 2011 Q2

EdexcelOld spec9 marksTransportation Problems

2. 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.

ABCSupply
131293220
222332722
325273220
423263838
Demand352530
(a) Add a dummy demand point and appropriate values to Table 1 in the answer book. (1)

Table 2 shows an initial solution given by the north-west corner method.
Table 3 shows some of the improvement indices for this solution.

ABCD
120
2157
3182
42810

Table 2

ABCD
1−13−9
2−11
3
41−7

Table 3

(b) Calculate the shadow costs and the missing improvement indices and enter them into Table 3 in the answer book. (4)
(c) Taking the most negative improvement index to indicate the entering square, use the stepping-stone method once to obtain an improved solution. You must make your route clear and state your entering cell and exiting cell. (4)
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