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A-Level MathematicsYear 2020Q7

8 P62682RA 7. A manufacturer can export five batches of footwear each year. Each exported batch contains just one type of footwear. The types of footwear are trainers, sandals or high heels. The table below shows the profit, in £1000s, for the number of batches of each type of footwear. Number of batches 0 1 2 3 4 5 Trainers 0 50 90 170 225 295 Sandals 0 70 110 165 245 300 High heels 0 75 115 x 235 305 The total annual profit is to be maximised. (a) Use dynamic programming to determine the two possible values of the maximum total annual profit, giving one of these values in terms of x. (10) Given that the maximum total annual profit is £320 000 (b) advise the manufacturer on the possible ways in which the five batches should be allocated. (2) (Total for Question 7 is 12 marks) TOTAL FOR PAPER IS 75 MARKS Please check the examination details below before entering your candidate information Candidate surname Other names Total Marks Centre Number Candidate Number Pearson Edexcel Level 3 GCE Answer Book Do not return the question paper with the answer book Further Mathematics Advanced Paper 4D: Decision Mathematics 2 Paper Reference 9FM0/4D Tuesday 23 June 2020 Afternoon (Time: 1 hour 30 minutes) P62682RA ©2020 Pearson Education Ltd. 1/1/1/1/1/1/ Turn over 2 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 1. 1 2 3 4 A 29 20 – 23 B 32 30 28 – C 35 32 34 25 D 29 31 27 30 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 __________________________________ 3 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 1 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 (Total for Question 1 is 8 marks) 4 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 2. A C B 0.6 0.4 0.75 0.25 0.8 0.2 350 −140 260 −190 220 −230 Figure 1 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 5 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 2 continued A C B 0.6 0.4 0.75 0.25 0.8 0.2 350 −140 260 −190 220 −230 Figure 1 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (Total for Question 2 is 7 marks) 6 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 3. 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 P Q R A B C D P Q R A B C D P Q R A B C D P Q R A B C D 7 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 3 continued P Q R A B C D P Q R A B C D P Q R A B C D P Q R A B C D P Q R A B C D 8 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 3 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 9 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 3 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (Total for Question 3 is 16 marks) 10 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 4. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 11 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 4 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (Total for Question 4 is 8 marks) 12 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 5. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 13 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 5 continued _ _ _ _ _ _ _ _ _ _ _ _ A D C B E F G H J Diagram 1 _ _ _ _ _ _ _ _ _ _ (Total for Question 5 is 10 marks) 14 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 6. Player B Option X Option Y Option Z Player A Option Q 1 5 3 Option R 4 −3 1 Option S 2 −4 −2 Option T 3 −2 0 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 15 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 6 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 16 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 6 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 17 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 6 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (Total for Question 6 is 14 marks) 18 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 7. Stage State Action Destination Value Trainers 0 0 0 0 19 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 7 continued Stage State Action Destination Value _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 20 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 12 marks) TOTAL FOR PAPER IS 75 MARKS

Paper Source:9FM0_4D_que_20201024.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)