CSIT113: Problem Solving - Knights and Knaves Island - Case Study - Management Assignment Help

Assignment Task:

Task:

Part A: 6 marks
On Knights and Knaves Island, a native can only be a knight or a knave. Both knights and knaves know everything. Knights always speak truth, knaves always lie. You meet two islanders, Alice and Bob, who make the following statements:
Alice: “One of us is a knight and one of us is a knave.”
Bob: “That’s right.”
a) Explain how you can identify Alice and Bob as a knight or a knave, using brute force with a truth table for Alice and Bob. (2 marks)
b) Explain how you can identify Alice and Bob, with a sequence of logical conclusions from the statements (calculational logic). Do not use brute force by taking different assumptions and then eliminating them. (You may / may not use symbols) (3 marks)
c) Carol, another person you meet on the Island, says “Bob will agree that I am a knight”. What is Carol? Explain you reasoning. (1 marks)

Part B: 6 marks
Questions a to f all refer to the following graph. Yes/No answers without an explanation carries no mark.

a) Is this graph weighted? Explain your answer. (0.5 mark)
b) Is this graph complete? Explain your answer. (0.5 mark)
c) Is this graph acyclic? Explain your answer. (0.5 mark)
d) Is this graph directed? Explain your answer. (0.5 mark)
e) Construct a minimal spanning tree using the node-at-a-time algorithm, starting at node A. List each added edge, in the order in which they are added by specifying the pair of nodes it joins (e.g. A-D). (2 marks)

f) Construct a maximal spanning tree (the tree with maximum weight) using the edge- at-a-time algorithm. List each added edge, in the order in which they are added by specifying the pair of nodes it joins (e.g. C-G). (2 marks)

Part C: 6 marks
A factory produces widgets. It has got several orders; each order is about a single widget. For each order, we know the following information:
i) The profit that this widget will generate.
ii) The deadline – the last day, until the end of which, the customer will accept delivery.
The factory can make exactly one widget per day. The following table shows all the orders for a 5- day period.
Order# 1 2 3 4 5 6 7 8 9 10
Profit 42 59 54 95 84 66 33 80 64 75
Deadline 2 5 3 4 5 3 2 4 1 2
a) Explain a strategy that can be used, for all similar problems with more or less orders, so as to maximise profit? Provide a clear and concrete explanation of your strategy. (4 marks)
b) By applying the strategy above, show the sequence in which orders should be chosen each day, for the company, to maximize the profit? What is the maximum profit the company can make with the given orders? (2 marks)

Part D: 6 marks
A factory has five workers, Anne, Bob, Carol, Dave and Ethan. It also has 5 tasks which must be done. Each worker does the tasks with a different efficiency. Apply the branch and bound strategy to allocate the tasks with minimum overall cost, when each task must be completed by a different worker.
The cost for each worker to do the tasks is given in the following table:

Task 1 Task 2 Task 3 Task 4 Task 5
Anne $4.00 $8.00 $8.00 $3.00 $4.00
Bob $9.00 $5.00 $5.00 $2.00 $7.00
Carol $4.00 $2.00 $4.00 $1.00 $3.00
Dave $7.00 $9.00 $6.00 $5.00 $8.00
Ethan $3.00 $6.00 $4.00 $4.00 $5.00
a) Describe a suitable method to calculate the lower bound value for all similar problems, where the total number of workers and the total number of tasks are equal? (1 mark)
b) Describe a method to calculate a suitable upper bound for similar problems? (1 mark)
c) Use the branch and bound strategy to find the most cost-efficient allocation of tasks to workers. Show the details of the expansion and pruning (branch and bound) of the decision tree along with reasons. (4 marks)

Part E: 6 marks
The Figure below shows a staircase region. The breadth and height of the region can be calculated using the small squares which fill it. For the below region, the breadth and height can be calculated as the sum of a side of 8 small squares. Let us call this staircase region, S8 (i.e., n = 8). Now, let us consider the general case. Find all values of n, where n>1, where a staircase region Sn can be completely tiled with the given triomino. The triomino is shown to the right (you may rotate it). (2 marks)

Prove your finding using any appropriate strategy. Use clear, concrete arguments applicable to general cases. (4 marks)

This CSIT113: Management Assignment has been solved by our Management  Experts at My Uni Paper. Our Assignment Writing Experts are efficient to provide a fresh solution to this question. We are serving more than 10000+ Students in Australia, UK & US by helping them to score HD in their academics. Our Experts are well trained to follow all marking rubrics & referencing style.

Be it a used or new solution, the quality of the work submitted by our assignment experts remains unhampered. You may continue to expect the same or even better quality with the used and new assignment solution files respectively. There’s one thing to be noticed that you could choose one between the two and acquire an HD either way. You could choose a new assignment solution file to get yourself an exclusive, plagiarism (with free Turnitin file), expert quality assignment or order an old solution file that was considered worthy of the highest distinction.