A2 June 2024 Q3

EdexcelCurrent spec12 marksTransportation Problems

3. The table below shows the cost, in pounds, of transporting one unit of stock from each of four supply points, E, F, G and H, to three sales points, A, 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.

ABCSupply
E23282221
F26192932
G29242029
H24261923
Demand451923
(a) Explain why it is necessary to add a dummy demand point. (1)
(b) On Table 1 in the answer book, insert appropriate values in the dummy demand column, D. (1)
ABCDSupply
E23282221
F26192932
G29242029
H24261923
Demand451923

Table 1

After finding an initial feasible solution and applying one iteration of the stepping-stone method, the table becomes

ABCD
E21
F1913
G623
H518
(c) 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
(6)
(d) State the cost of the solution found in (c). (1)
(e) Determine whether the solution obtained in (c) is optimal, giving a reason for your answer. (3)
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