4 P62682RA 3. 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 three sales points, P, Q and R. 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 Supply A 25 24 17 42 B 7 12 14 68 C 13 11 20 25 D 16 15 13 40 Demand 59 72 44 Table 1 Table 2 shows an initial solution given by the north-west corner method. P Q R A 42 B 17 51 C 21 4 D 40 Table 2 (a) Taking AR as the entering cell, use the stepping-stone method to find an improved solution. Make your method clear. (2) (b) Perform one further iteration of the stepping-stone method to obtain an improved solution. You must make your method clear by stating ●  shadow costs ●  improvement indices ●  route ●  entering cell and exiting cell. (4) (c) Determine whether the solution obtained from this second iteration is optimal, giving the reason for your answer. (3) (d) Formulate this situation as a linear programming problem. You must define your decision variables and make the objective function and constraints clear. (6) (e) Explain why the Simplex algorithm cannot be used to solve transportation linear programming problems such as that formulated in (d). (1) (Total for Question 3 is 16 marks)