
Module D1 Decision Mathematics Questions
Handful of easy questions designed for students wishing to catch up on the D1 module, or simply for those interested who never studied Decision Mathematics. Questions will all be relatively easy.
1) The marks obtained in an examination by five students were;
Anne (68), Barry (42), Clare (70), David (45), Eileen (50) and Greg (55).
Use the bubblesort algorithm to sort these marks (a) in ascending order (b) in descending order
2) Use the quicksort algorithm to sort the list
6, 8, 4, 5, 10, 2, 9
in ascending order.
3) The members of a club have surnames
Monro, Jones, Malik, Wilson and Shah
Use the bubblesort algorithm to sort these into alphabetical order.
4) Use the bubblesort algorithm to sort these into alphabetical order;
4, 3, 5, 0, 2, 5, 1
5) The times recorded by seven competitors for a given distance were;
9.8, 9.2, 9.6, 9.7, 9.1, 8.9, 9.0
(a) Use the bubblesort algorithm to sort these times into order. (b) Use the quicksort algorithm to sort the times into ascending order. (c) Which of the methods is more efficient in this case?
Re: Module D1 Decision Mathematics Questions
6) A project is to be completed in 13 days. The activities involved in the project and their durations in days are given in the list
A  3 B  8 C  7 D  5 E  8 F  4 G  5 H  4 I  4 J  4
To determine how many workers are required;
(a) Apply the firstfit algorithm (b) Apply the firstfit decreasing algorithm (c) Is it possible to obtain a better solution than either (a) or (b)?
7) A small ferry that sails between two of the islands in the Hebrides has three lanes 20 metres long on its car deck. The vehicles waiting to be loaded are;
Petrol Tanker  13m Small Truck  6m Car  4m Small Van  3m Coach  12m Lorry  11m Truck  7m Car  3m
(a) Can you use the firstfit decreasing algorithm to load all the vehicles on to the ferry? (b) Can all te vehicles be taken in one trip?
8) A project consists of eight activities whose durations in hours are as follows;
A  2 B  4 C  3 D  1 E  5 F  4 G  2 H  3
Use fullbin combinations to determine the minimum number of workers needed to finish the project in 12 hours.
8) A certain kind of pipe is sold in 10m lengths. For a particular job the following lengths are required;
2m, 8m, 4m, 5m, 2m, 5m, 4m
By looking for fullbin combinations, or otherwise, find the number of 10m lengths required for the job.
9) Joan decided that she wanted to record a number of programmes on the video recorder. The lengths of the programmes were;
45 min, 1h, 35min, 15min, 40min, 30min, 50min, 55min and 25min.
Help Joan decide how many 2h tapes she requires, using;
(a) The firstfit algorithm (b) The firstfit decreasing algorithm (c) Fullbin combinations
10) 120, 78, 100, 90, 60, 38, 80, 26, 150
(a) The list of numbers above is to be sorted into descending order. Perform a quicksort to obtain the required list. Give the state of the list after each rearrangement and indicate clearly the pivot elements used. (b) (i) Use the firstfit decreasing algorithm to fit the data into bins of size 200. (ii) Explain how you decided into which bin to place the number 78.
Re: Module D1 Decision Mathematics Questions
wow its interesting ... i like to solve such problems but is difficult for me can you answer plz..
 bobbym
 Administrator
Re: Module D1 Decision Mathematics Questions
Hi john2kin;
Welcome to the forum and Merry Christmas!
9) Joan decided that she wanted to record a number of programmes on the video recorder. The lengths of the programmes were;
45 min, 1h, 35min, 15min, 40min, 30min, 50min, 55min and 25min.
This is a bin packing problem. The first fit algorithm just takes them as you see them and puts them into the first available bin that they will fit.
Think of the tapes as bins that hold 120 minutes. So start packing.
1st bin: 45 min, 1 hr., 15 min.
2nd bin:35min, 40min, 30 min
3rd bin: 50 min, 55 min,
4th bin: 25 min.
Answer she needs 4 tapes. The algorithm may not have provided the optimum answer but it did provide an answer.
The firstfit decreasing algorithm, sorts the list first, largest to smallest. Then applies the above first fit algorithm.
Bin 1) 60 min, 55min Bin 2) 50min, 45min, 15min Bin 3) 40min, 35min, 30min Bin 4) 25 min
This also requires four tapes.
Can you find a tighter packing than both of these algorithms?
In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
