A2 October 2021 Q3

EdexcelCurrent spec11 marksTransportation Problems

3. The table below shows the cost, in pounds, of transporting one unit of stock from each of four supply points, A, B, C and D, to four sales points, P, Q, R and S. It also shows the number of units held at each supply point and the number of units required at each sales point.

A minimum cost solution is required.

PQRSSupply
A1819171328
B1615141943
C2117222329
D1620192136
Demand25414030
(a) Use the north-west corner method to obtain an initial solution. (1)
(b) Taking AS as the entering cell, use the stepping-stone method to find an improved solution. Make your method clear. (2)
(c) Perform one further iteration of the stepping-stone method to obtain an improved solution. You must make your method clear by showing the route and stating the
  • shadow costs
  • improvement indices
  • entering cell and exiting cell
(4)
(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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