OCR 2023 GCE FURTHER MATHEMATICS B MEI Y433/01: MODELLING WITH ALGORITHMS A LEVEL QUESTION PAPER & MARK SCHEME (MERGED

Ten suitcases are to be transported in containers. Each container can hold a maximum of n kg, where n is a positive integer. The total weight of the ten suitcases is 216kg. You are given that at least 4 containers are needed to transport all ten suitcases. (a) Determine the maximum value of n for which any set of 10 suitcases with total weight 216 kg needs at least 4 containers. [2] The exact weights, in kg, of the suitcases are: (b) Apply the quick sort algorithm to sort the list of numbers into descending order. You should use the first value as the pivot for each sublist. [3] The first fit decreasing algorithm is applied to the sorted list of numbers. The following allocation of suitcases to containers is obtained. Container 1: 31 27 Container 2: 26 24 18 Container 3: 23 21 17 Container 4: 15 14 (c) Determine the possible values of n that are consistent with this result from applying the first fit decreasing algorithm to the sorted list of these weights. [2] 3 © OCR 2023 Y433/01 Jun23 Turn over 2 The diagram shows an activity network for a project. The arc weights show activity durations in hours. The numbers in circles are event numbers. A(5) 2 D(4) E(10) F(12) K(11) 5 8 L(4) J(4)