2 P66804A 1. Four workers, A, B, C and D, are to be assigned to three tasks, 1, 2 and 3. Each task must be assigned to just one worker and each worker can do one task only. Worker A cannot do task 2 and worker D cannot do task 3 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 A 53 – 62 B 48 57 59 C 55 63 58 D 69 49 – Formulate the above situation as a linear programming problem. You must define your decision variables and make the objective function and constraints clear. (6) (Total for Question 1 is 6 marks) 2. Alka is considering paying £5 to play a game. The game involves rolling two fair six‑sided dice. If the sum of the numbers on the two dice is at least 8, she receives £10, otherwise she loses and receives nothing. If Alka loses, she can pay a further £5 to roll the dice again. If both dice show the same number then she receives £35, otherwise she loses and receives nothing. (i) Draw a decision tree to model Alka’s possible decisions and the possible outcomes. (ii) Determine Alka’s optimal EMV and state the optimal strategy indicated by the decision tree. (7) (Total for Question 2 is 7 marks)