D2 June 2018 Q1

EdexcelOld spec7 marksTransportation Problems

1. Table 1 shows the cost, in pounds, of transporting one unit of stock from each of four supply points, A, B, C and D, to each of four demand points, 1, 2, 3 and 4. It also shows the stock held at each supply point and the stock required at each demand point. A minimum cost solution to this transportation problem is required.

1234Supply
A2432213427
B2831293741
C2541333531
D2332313614
Demand33352520

Table 1

Table 2 shows an initial solution given by the north-west corner method.

1234
A27
B635
C0256
D14

Table 2

(a) Explain why a zero has been placed in cell C2 in Table 2. State the other cell in Table 2 in which the zero could have been placed. (2)
(b) State the shadow costs clearly and enter the improvement indices into Table 3 in your answer book. (3)

Taking the most negative improvement index to indicate the entering cell,

(c) list the stepping-stone route that should be used to obtain the next solution. You should make clear the cells that are included in your route and state your entering and exiting cells. [You do not need to state the next solution. You do not need to solve this problem.] (2)
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