Assignments

Question 1

A study was conducted to investigate the relationship between the amount spent on construction materials in projects and the corresponding revenue generated from projects. Data on the projects completed by ten different construction companies are shown in the table below.

Using the dataset, calculate the correlation coefficient between the two variables and provide your interpretation on it. Taking revenue as the dependent variable, develop a simple linear regression model, and estimate the revenue of a company if the amount spent on construction materials is £710,000.

Question 2

A building company constructs two roof models (A and B) and the profit per roof sold is £3000 and £5000 respectively. Each roof model has to be assembled on a particular machine, each model A takes 15 minutes of assembly time and each model B takes 25 minutes of assembly time. The company estimates that the machine used for assembly has an effective working week of only 30 hours (due to maintenance/breakdown). There are some technical constraints that require producing at least two units of product model B for every five units of model A produced. There are also marketing requirements that at least 30 units of model A and 20 units of model B need to be produced every week. Develop an LP model for this problem to determine how many units of the two roof models should be produced each week in order to maximise the profit.

Question 3

Traffic congestion is a recurring problem in growing cities. Most often, in order to deal with the problem, the authority would address the supply side of road infrastructure and increase the road capacity to bear the increasing traffic pressure. This particular policy is found to be often counterintuitive. By using a set of causal feedback loop diagram, explain how the implementation of the policy could turn out to be ineffective and at times counterproductive as well.

Question 4

A required compressive strength test of concrete specimens was carried out at a construction site. The result of standard 28-day cube tests on 30 different samples of M15 grade concrete revealed that the mean compressive strength of the sample cubes was 15.05 N/mm2 with a standard deviation of 2.89 N/mm2. The minimum required compressive strength of the concrete grade is 15N/mm2. Find out whether the concrete being used at the site meet the minimum strength requirement. Use the significance level of 0.05 for your analysis.

Question 5

A company wants to investigate how the change in sales is reflected in its income.The following data for five years are available. Knowing that there is a linear relationship between sales and income,

1. calculate the coefficient of correlation (r), and provide its interpretation
2. find the equation of the best fit line to this set of data
3. using the equation in part (b), predict the company’s income if the sales are 24.2 thousand pounds.

Question 6

A company manufactures two products (A and B) and the profit per unit sold is £30 and £50 respectively. Each product has to be assembled on a particular machine, each unit of product A taking 10 minutes of assembly time and each unit of product B 25 minutes of assembly time. The company estimates that the machine used for assembly has an effective working week of only 30 hours (due to maintenance/breakdown).

There are technological constraints which mean that for every five units of product A produced at least two units of product B must be produced. Moreover, in order to satisfy the shipping contract, a total of at least 50 products much be shipped each week. How many of each product needs to be produced in order to maximise the total profit?

1. Formulate the problem of maximising the profit as a linear programme.
2. Solve this linear programme graphically.

Question 7

You are a project manager in the process of developing the schedule for your project. A task lead on your project reports that in order to complete a particular task, it will take him at least 22 days. You suspect that his claim is not correct. In order to validate your assertion, you examined 10 similar tasks and found that the mean duration is 20 days with a standard deviation of 1.5 days. Is there enough evidence to reject the team lead’s claim at the significance level of 0.05? Assume the probability distribution to be normal.

Question 8

A goal-seeking feedback loop (FBL) is shown below in the diagram. Sketch the pattern of planned “Works Done” over time. If there are reworks to be done due to various errors during execution of project works, provide any two ideas for decisions to act upon so that the scope of work could be completed without or with a minimum possible delay. Discuss your decisions on the basis of the given FBLdiagram.

Question 9

1. Describe in detail mental model by providing the definition of the model terminology, explanation and sample cases.
2. Explain how the systems thinking approach could help to enrich and broaden the mental model for making better decisions.

Question 10

Quantum Corp., a small firm, has developed new software for organizing and playing music on a computer. The software contains a number of unique features that have been patented. However, there now has been an ominous development. It appears that a number of the patented features were copied in similar software developed by Xactiq Corp., a huge software company with annual sales revenue in excess of £1 billion. In response, Quantum Corp. has sued Xactiq Corp for patent infringement. With attorney fees and other expenses, the cost of going to trial(win or lose)is expected to be £1 million. Quantum Corp. feels that it has a 60% chance of winning the case, in which case it would receive £5 million in damages. If it loses the case, it gets nothing. Moreover, if it loses the case, there is a 50% chance that the judge would also order Quantum Corp. to pay for court expenses and lawyer fees for Xactiq Corp. (an additional £1 million cost). Xactiq Corp. has offered Quantum Corp. £1.5 million to settle this case out of court.

1. Draw a decision tree to represent this problem.
2. Which alternative is the best choice? Kindly explain.
3. Draw a sensitivity analysis plot with respect to the probability of winning at trial. Identify the critical points on the plot and discuss the best choices for different cases.