3 Turn over P66804A 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. P Q R S Supply A 18 19 17 13 28 B 16 15 14 19 43 C 21 17 22 23 29 D 16 20 19 21 36 Demand 25 41 40 30 (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) (Total for Question 3 is 11 marks)