8 P61182A 7. A shop sells two types of watch, analogue watches and digital watches. The shop manager knows that, each month, she should order at least 60 watches in total. In addition, at most 80% of the watches she orders must be digital. Let x be the number of analogue watches ordered and let y be the number of digital watches ordered. (a) Write down inequalities, in terms of x and y, to model these constraints. (2) Two further constraints are y + 3x . 140 4y + x . 80 (b) Represent all these constraints on Diagram 1 in the answer book. Hence determine, and label, the feasible region, R. (4) The cost to the shop of ordering an analogue watch is five times the cost of ordering a digital watch. The shop manager wishes to minimise the total cost. (c) Determine the number of each type of watch the shop manager should order. You must make your method clear. (3) Given that the minimum total cost of ordering the watches is £4455 (d) determine the cost of ordering one analogue watch and the cost of ordering one digital watch. You must make your method clear. (3) (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 P61182A ©2019 Pearson Education Ltd. 1/1/1/1/1/1/C2/1/ Turn over Answer Book Do not return the question paper with the answer book. Paper Reference 9FM0/3D Morning (Time: 1 hour 30 minutes) Monday 24 June 2019 Turn over Further Mathematics Advanced Paper 3D: Decision Mathematics 1 2 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 1. 2.1 1.7 3.0 1.9 3.2 1.2 3.3 1.4 1.5 0.2 _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 3 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 1 continued 2.1 1.7 3.0 1.9 3.2 1.2 3.3 1.4 1.5 0.2 _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (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. Vertex Order of labelling Final value Working values Key: B E D J H F A C G 38 42 15 10 17 14 6 23 39 12 7 20 42 75 10 Shortest path from A to D: ________________________________________________________ Length of shortest path from A to D: ________________________________________________ 5 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 2 continued H C G E J D B A F 38 75 42 15 10 42 20 12 10 17 14 23 6 39 7 Figure 1 _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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THIS AREA DO NOT WRITE IN THIS AREA Question 2 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 2 is 14 marks) 8 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 3. (a) Initial distance table Initial route table A B C D E A B C D E A A B B C C D D E E (b) 1st iteration Distance table Route table A B C D E A B C D E A A B B C C D D E E 2nd iteration Distance table Route table A B C D E A B C D E A A B B C C D D E E 3rd iteration Distance table Route table A B C D E A B C D E A A B B C C D D E E Turn to page 11 for spare copies of these tables if you need to correct your work. 9 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 3 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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THIS AREA DO NOT WRITE IN THIS AREA Question 3 continued Only use these tables if you need to correct your work. (a) Initial distance table Initial route table A B C D E A B C D E A A B B C C D D E E (b) 1st iteration Distance table Route table A B C D E A B C D E A A B B C C D D E E 2nd iteration Distance table Route table A B C D E A B C D E A A B B C C D D E E 3rd iteration Distance table Route table A B C D E A B C D E A A B B C C D D E E (Total for Question 3 is 14 marks) 12 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 4. Early event time Late event time Key: 25 A(8) D(11) I(6) E(5) K(6) J(4) L(7) F(8) B(6) C(7) G(10) H(x) M(6) Diagram 1 _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 5 is 6 marks) 16 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 6. _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ (b) b.v. x y z s1 s2 s3 a1 a2 Value 30 8 15 P Only use the tableau below if you need to correct the above tableau. b.v. x y z s1 s2 s3 a1 a2 Value 30 8 15 P 18 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 6 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 6 is 12 marks) 20 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 7. _____________________________________________________________________________________ _____________________________________________________________________________________ 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THIS AREA DO NOT WRITE IN THIS AREA Question 7 continued Turn to page 24 for a spare copy of these axes if you need to correct your work. 0 10 20 30 40 50 60 70 80 90 100 Diagram 1 0 20 40 60 80 100 120 140 160 y x 22 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 7 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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160 y x (Total for Question 7 is 12 marks) TOTAL FOR PAPER IS 75 MARKS