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# Quantitative Methods for Property Studies

School of Civil Engineering

 and Surveying Coursework self-assessment sheet for students Student Registration Number: Date: Unit Name Quantitative Methods for Property Studies Artefact Item 2 – Coursework The University of Portsmouth regulations require students to keep electronic copies of all assignments, and submit these at any time upon request. Shaded areas to be completed by student and this sheet submitted with assignment.

 Student comment: I have read and understood the University’s regulations on plagiarism – please type an ‘x’ Criteria Description Weighting % Student Evaluation (to be completed before submission) (enter an ‘x’ in required boxes) Pass Fail A* A B C D E F Question 1 (LO 3,6) Linear programming and decision analysis 45 Question 2 (LO 5,7) Critical path analysis and calculations of properties of materials 30 Question 3 (LO 4) Forecasting 25

 Overall Grade (to be completed before submission) Letter Grade (A* – F) Percentage (100 – 0)

Key: A*: 80% or above, A: 70% – 79%, B: 60% – 69%, C: 50% – 59%, D: 40% – 49%, E: 30% – 39%, F: 29% or less
IMPORTANT: See separate Grade Criteria for characteristics of work in the above grades

 Student Comment (to be completed before submission)

# Instructions

cover sheet) to the Turnitin box on Moodle by 11pm on
Tuesday 27th March 2018.
Question 1
A developer plans to convert a small disused warehouse into a number of studios for local artists. To
support the development, they will also include at least one retail unit. The space available could be
developed into a maximum of four retail units or 24 studios. There is a restriction on the availability
of specialised labour, with a maximum of 500 hours. Each retail unit would require 100 hours of
specialised labour, whereas each studio would require 25 hours. A restriction required by the local
council is that there must be no more than one retail unit for every five studios.
The monthly rent chargeable for each retail unit is £1000, and the monthly rent chargeable for each
studio is £200.
(a) Formulate this problem as a linear programming plot, and determine the optimal number of
retail units and studios that the council should include in the development in order to maximise
rental income. Explain your decision, and state the maximum monthly rental income.
[15 marks]
(b)
Market research suggests that such studios are in demand, and so a higher rent could be
charged. How high would the monthly rent for the studios need to increase to for you to change
your decision on the optimal number of rental units and studios? What would your new
[15 marks]
(c)
The developer is considering applying for £5000 of funding to support the project. If they submit
an initial outline bid, they will incur a cost of £50. The probability of then being invited to submit a
full bid is 0.1. At this stage, if they were to choose to submit a full bid, they would incur a cost of
£200. The probability of a full bid being successful is 0.25. Represent this problem as a decision tree,
and calculate the expected value of submitting an initial outline bid.
[15 marks]
Question 2
The tasks that form a phase of the project are listed below, with their durations and dependencies.

 Task Dependencies Duration (days) A – 2 B – 4 C A 5 D – 1 E C 2 F D 2 G B 2 H B,F 6 I G 2

(a) Construct a critical path network diagram for these tasks, and calculate the total float for each
task. Find the critical path, and determine the total duration of this phase of the project.
[18 marks]
(b)
The duration of Task H has been revised to 4 days. Explain the impact (if any) this will have on the
overall duration of this phase of the project.
[5 marks]
(c)
The concrete mix for this phase of the project will be in the ratio 1:4:4 by volume (cement: sand:
aggregate). Cement has density 1.414 tonnes per m
3. Calculate the mass of cement (tonnes)
required for X.Y m
3 of concrete, where X and Y are the first and second digits of your student
[7 marks]
Question 3
Sales figures (£) for a retailer from the past six years are shown in the table below. Using Excel,
analyse this data with deseasonalised moving average techniques, and report your results.
Include: