> Wednesday 20 October 2021 – Afternoon A Level Further Mathematics B (MEI) Y433/01 Modelling with Algorithms. GRADED A+
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Answer all the questions.
1 The list below shows the sizes of 13 items.
5 16 12 15 21 10 17 5 3 6 13 24 5
(a) Show the result of applying the first fit algorithm to pack items with the sizes listed
...
above into
bins that have a capacity of 45. [2]
(b) Show the result of applying a full bin strategy to pack items with the sizes listed above into
bins that have a capacity of 45. [2]
2 The table below shows the activities involved in a project, together with their immediate
predecessors. The table also gives the duration (in hours) of each activity, apart from G and H.
Activity Immediate predecessors Duration (hours)
A – 6
B – 4
C – 8
D C 3
E A, B, D 6
F B, D 10
G C
H C
I E, F, G 10
J F, G 7
K F, G, H 9
(a) Draw an activity network, using activity on arc, to represent the project. [3]
It is given that the only critical activities of the project are C, D, F, and I.
(b) Carry out a forward pass and a backward pass through the activity network, showing the early
event time and late event time at each vertex of your network. [3]
(c) State the minimum completion time for the project. [1]
(d) Calculate the interfering float at H, given that the independent float is not 0. [1]
It is given that the total float of activity G is at most double the total float of activity E. Let x be the
duration, in hours, of activity G.
(e) Determine the range of possible values of x. [3]3
© OCR 2021 Y433/01 Oct21 Turn over
3 A vertex of a graph for which the order is an odd number is called an odd vertex.
(a) (i) By considering the number of arc endings for a general graph, explain why, for every
graph, the sum of the vertex orders must be an even number. [1]
(ii) Hence explain why no graph can have an odd number of odd vertices
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