8 P66804A 7. Alexis and Becky are playing a zero‑sum game. Alexis has two options, Q and R. Becky has three options, X, Y and Z. Alexis intends to make a random choice between options Q and R, choosing option Q with probability p1 and option R with probability p2 Alexis wants to find the optimal values of p1 and p2 and formulates the following linear programme, writing the constraints as inequalities. Maximise P = V where V = 3 + the value of the game to Alexis subject to V  6p1 + p2 V  8p2 V  4p1 + 2p2 p1 + p2  1 p1  0 , p2  0 , V  0 (a) Complete the pay‑off matrix for Alexis in the answer book. (2) (b) Use a graphical method to find the best strategy for Alexis. (6) (c) Calculate the value of the game to Alexis. (1) Becky intends to make a random choice between options X, Y and Z, choosing option X with probability q1 , option Y with probability q2 and option Z with probability q3 (d) Determine the best strategy for Becky, making your method and working clear. (3) (Total for Question 7 is 12 marks) TOTAL FOR PAPER IS 75 MARKS