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A-Level MathematicsYear 2023Q8

  9 P74086A 8. A two-person zero-sum game is represented by the pay-off matrix for player A shown below. Player A Player B Option X Option Q Option R Option S Option T −3 2 4 −4 Option Y 2 −1 −2 0 Option Z 5 0 −1 2 (a) Verify that there is no stable solution to this game. (2) (b) Explain why player A should never play option T. You must make your reasoning clear. (2) Player A intends to make a random choice between options Q, R and S, choosing option Q with probability p1, option R with probability p2 and option S with probability p3 Player A wants to calculate the optimal values of p1, p2 and p3 using the Simplex algorithm. (c) (i) Formulate the game as a linear programming problem for player A. You should write the constraints as equations. (ii) Write down an initial Simplex tableau for this linear programming problem, making your variables clear. (7) The linear programming problem is solved using the Simplex algorithm. The optimal value of p1 6 11 is and the optimal value of p2 0 is (d) Find the best strategy for player B, defining any variables you use. (6) (Total for Question 8 is 17 marks) TOTAL FOR PAPER IS 75 MARKS 10 P74086A   BLANK PAGE   11 P74086A BLANK PAGE 12 P74086A   BLANK PAGE Turn over P74086A ©2023 Pearson Education Ltd. N:1/1/1/1/1/1/   Please check the examination details below before entering your candidate information Candidate surname Other names Centre Number Candidate Number Pearson Edexcel Level 3 GCE Monday 26 June 2023 Afternoon (Time: 1 hour 30 minutes) 9FM0/4D Paper reference Total Marks Further Mathematics Advanced PAPER 4D: Decision Mathematics 2 Answer Book Do not return the question paper with the answer book. DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 2   1. C2 C2 C1 C1 A F T E C S B D 12 17 10 10 4 52 29 4 5 5 8 8 2 6 22 18 18 11 11 10 17 17 15 20 26 19 21 44 Figure 1 ___________________________________________ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Turn over 3   DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 1 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (Total for Question 1 is 7 marks) DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 4   2. _ _ _ _ _ Turn over 5   DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 2 continued Use the space below if you need to redraw your decision tree. (Total for Question 2 is 5 marks) DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 6   3. (a) _ _ _ _ _ _ _ _ _ _ _ _ (b) Q R S A B C D You may not need to use all of these tables. Q R S A B C D Q R S A B C D �� Turn over 7   DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 3 continued Q R S A B C D Q R S A B C D Q R S A B C D Q R S A B C D Q R S A B C D (Total for Question 3 is 9 marks) �� DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 8   4. 1 2 3 4 A 34 20 18 15 B 49 31 12 34 C 48 27 23 26 D 52 45 42 42 You may not need to use all of these tables. 1 2 3 4 A B C D 1 2 3 4 A B C D 1 2 3 4 A B C D 1 2 3 4 A B C D �� Turn over 9   DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 4 continued 1 2 3 4 A B C D 1 2 3 4 A B C D 1 2 3 4 A B C D 1 2 3 4 A B C D 1 2 3 4 A B C D (Total for Question 4 is 8 marks) �� DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 10   5. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Turn over 11   DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 5 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (Total for Question 5 is 8 marks) DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 12   6. Stage State Action Destination Value Turn over 13   DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 6 continued Stage State Action Destination Value _ _ _ _ _ _ _ _ _ _ _ _ (Total for Question 6 is 13 marks) DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 14   7. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Turn over 15   DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 7 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (Total for Question 7 is 8 marks) DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 16   8. Player A Player B Option X Option Q Option R Option S Option T −3 2 4 −4 Option Y 2 −1 −2 0 Option Z 5 0 −1 2 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Turn over 17   DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 8 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ b.v. Value P DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 18   Question 8 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Turn over 19   DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 8 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 20   Question 8 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ___________________________________________ (Total for Question 8 is 17 marks) TOTAL FOR PAPER IS 75 MARKS

Paper Source:EAMF3199fm0-4d-que-20230627.pdf

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Exam Specification Info

This question is part of the UK A-Level Mathematics syllabus. In the actual exam, structured questions typically require linking specific keywords to gain full marks. Applaa helps you drill these topics.

Syllabus levelAdvanced Level (A-Level)

SubjectMathematics

Official MarksVariable (2–6 marks)