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A-Level MathematicsYear 2019Q5

P61639A 5 5. Ben is a wedding planner. He needs to order flowers for the weddings that are taking place next month. The three types of flower he needs to order are roses, hydrangeas and peonies. Based on his experience, Ben forms the following constraints on the number of each type of flower he will need to order. Ɣ At least three-fifths of all the flowers must be roses. Ɣ For every 2 hydrangeas there must be at most 3 peonies. Ɣ The total number of flowers must be exactly 1000 The cost of each rose is £1, the cost of each hydrangea is £5 and the cost of each peony is £4 Ben wants to minimise the cost of the flowers. Let x represent the number of roses, let y represent the number of hydrangeas and let z represent the number of peonies that he will order. (a) Formulate this as a linear programming problem in x and y only, stating the objective function and listing the constraints as simplified inequalities with integer coefficients. (7) Ben decides to order the minimum number of roses that satisfy his constraints. (b) (i) Calculate the number of each type of flower that he will order to minimise the cost of the flowers. (ii) Calculate the corresponding total cost of this order. (3) (Total for Question 5 is 10 marks) TOTAL FOR DECISION MATHEMATICS 1 IS 40 MARKS END P61639A 6 BLANK PAGE P61639A 7 BLANK PAGE P61639A 8 BLANK PAGE Please check the examination details below before entering your candidate information Candidate surname Other names Total Marks Centre Number Candidate Number Answer Book Do not return the question paper with the answer book. Further Mathematics Advanced Subsidiary Further Mathematics options 27: Decision Mathematics 1 (Part of options D, F, H and K) Paper Reference 8FM0-27 Afternoon Thursday 16 May 2019 Pearson Edexcel Level 3 GCE P61639A ©2019 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. ___________________________________________ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 3 Turn over 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 6 marks) 4 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 2. You may not need to use all the rows in this table. It may not be necessary to complete all boxes in each row. A B N H C D E F Final output: 5 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 2 continued ___ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (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. 7 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 7 marks) 8 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 4. Vertex Order of labelling Final value Working values Key: C D H G F E B A 9 17 25 10 5 x + y 3x + y 16 3 9 2 13 12 7 7 9 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 10 marks) 10 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 5. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 11 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 5 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 12 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 10 marks) TOTAL FOR DECISION MATHEMATICS 1 IS 40 MARKS

Paper Source:8FM0_27_que_20190517.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)