Edexcel as level further mathematics question paper 28 may 2023

Pearson Edexcel Level 3 GCE Friday 19 May 2023 Afternoon Paper reference 8FM0/28 Further Mathematics Advanced Subsidiary Further Mathematics options 28: Decision Mathematics 2 (Part of option K only) You must have: Mathematical Formulae and Statistical Tables (Green), calculator, D2 Answer Book (enclosed) Candidates may use any calculator allowed by Pearson regulations. Calculators must not have the facility for symbolic algebra manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them. Instructions • Use black ink or ball‑point pen. • If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). • Fill in the boxes at the top of the answer book with your name, centre number and candidate number. • Answer all questions and ensure that your answers to parts of questions are clearly labelled. • Answer the questions in the answer book provided – there may be more space than you need. • You should show sufficient working to make your methods clear. Answers without working may not gain full credit. • Inexact answers should be given to three significant figures unless otherwise stated. • Do not return the question paper with the D2 Answer Book. Information • A booklet ‘Mathematical Formulae and Statistical Tables’ is provided. • The total mark for this part of the examination is 40. There are 4 questions. • The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question. Advice • Read each question carefully before you start to answer it. • Try to answer every question. • Check your answers if you have time at the end. P72814A ©2023 Pearson Education Ltd. N:1/1/1/1/2 P72814A  1. Five workers, A, B, C, D and E, are available to complete four tasks, P, Q, R and S. Each worker can only be assigned to at most one task, and each task must be done by at most one worker. Worker B cannot be assigned to task Q and worker E cannot be assigned to task S. The time, in minutes, that each worker takes to complete each task is shown in the table below. P Q R S A B 39 – 39 40 C D E 36 39 41 – The Hungarian algorithm is to be used to find the least total time to complete all four tasks. (a) Explain how the table should be modified so that the Hungarian algorithm can be applied. (2) (b) (i) Use the Hungarian algorithm to obtain an allocation that minimises the total time. (ii) Explain how you determined if the table was optimal at each stage. (6) (c) Calculate the least total time to complete all four tasks. (1) (Total for Question 1 is 9 marks) 3 Turn over P72814A 2. S A B C D E F G H 7 15 18 32 8 18 18 17 1 39 5 6 4 2 3 21 0 2 0 0 7 28 36 64 0 4 0 9 0 31 0 0 8 8 5 5 J T 2 13 Figure 1 An engineer monitors a system of pipes through which a fluid flows from the source, S, to the sink, T. The engineer initialises the labelling procedure for this system, and the excess capacities and potential backflows are shown on the arrows either side of each arc, as shown in Figure 1. (a) State the value of the initial flow. (1) (b) Obtain the capacity of the cut that passes through the arcs SA, SB, CE, FE and FJ. (1