2 P72118A 1. Four workers, A, B, C and D, are to be assigned to four tasks, 1, 2, 3 and 4. Each task must be assigned to just one worker and each worker must do only one task. The cost of assigning each worker to each task is shown in the table below. The total cost is to be minimised. 1 2 3 4 A 32 45 34 48 B 37 39 50 46 C 46 44 40 42 D 43 45 48 52 (a) Reducing rows first, use the Hungarian algorithm to obtain an allocation that minimises the total cost. You must make your method clear and show the table after each stage. (5) (b) State the minimum total cost. (1) (Total for Question 1 is 6 marks) 2. The general solution of the second order recurrence relation un + 2 + k1un + 1 + k2un = 0 n  0 is given by un = (A + Bn)(–3)n where A and B are arbitrary non‑zero constants. (a) Find the value of k1 and the value of k2 (2) Given that  u0 = u1 = 1 (b) find the value of A and the value of B. (2) (Total for Question 2 is 4 marks)