9 P66801A 8. Susie is preparing for a triathlon event that is taking place next month. A triathlon involves three activities: swimming, cycling and running. Susie decides that in her training next week she should • maximise the total time spent cycling and running • train for at most 39 hours • spend at least 40% of her time swimming • spend a total of at least 28 hours of her time swimming and running Susie needs to determine how long she should spend next week training for each activity. Let • x represent the number of hours swimming • y represent the number of hours cycling • z represent the number of hours running (a) Formulate the information above as a linear programming problem. State the objective and list the constraints as simplified inequalities with integer coefficients. (5) Susie decides to solve this linear programming problem by using the two-stage Simplex method. (b) Set up an initial tableau for solving this problem using the two-stage Simplex method. As part of your solution you must show how • the constraints have been made into equations using slack variables, exactly one surplus variable and exactly one artificial variable • the rows for the two objective functions are formed (6) The following tableau T is obtained after one iteration of the second stage of the two‑stage Simplex method. b.v. x y z s1 s2 s3 Value y 0 1 0 1 0 1 11 s2 0 0 5 −2 1 −5 62 x 1 0 1 0 0 −1 28 P 0 0 −1 1 0 1 11 (c) Obtain a suitable pivot for a second iteration. You must give reasons for your answer. (2) (d) Starting from tableau T, solve the linear programming problem by performing one further iteration of the second stage of the two-stage Simplex method. You should make your method clear by stating the row operations you use. (5) (Total for Question 8 is 18 marks) TOTAL FOR PAPER IS 75 MARKS 10 P66801A BLANK PAGE 11 P66801A BLANK PAGE 12 P66801A BLANK PAGE Turn over Pearson Edexcel Level 3 GCE Candidate surname Other names Total Marks Centre Number Candidate Number Please check the examination details below before entering your candidate information Time Paper reference P66801A ©2021 Pearson Education Ltd. 1/1/1/1/ Answer book Do not return the question paper with the answer book. Further Mathematics Advanced PAPER 3D: Decision Mathematics 1 9FM0/3D 1 hour 30 minutes 2 1. A B C D E U V W X Y Figure 1 _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________