OCR MEI D2 2008 June — Question 2 16 marks

Exam BoardOCR MEI
ModuleD2 (Decision Mathematics 2)
Year2008
SessionJune
Marks16
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCombinations & Selection
TypeBasic committee/group selection
DifficultyEasy -1.8 This is a straightforward decision tree question requiring only basic arithmetic and tree construction. Part (i) involves simple cost calculations (£500+£600=£1100 vs £900), part (ii) adds one probability layer (0.5 each for 2 or 4 trips), and part (iii) asks for a textbook definition of EMV. No complex probability, combinatorics, or problem-solving insight needed—purely mechanical application of a standard D2 technique.
Spec7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities7.05d Latest start and earliest finish: independent and interfering float7.05e Cascade charts: scheduling and effect of delays
2 Jane has a house on a Mediterranean island. She spends eight weeks a year there, either visiting twice for four weeks each trip or four times for two weeks each trip. Jane is wondering whether it is best for her to fly out and rent a car, or to drive out.
Flights cost \(\pounds 500\) return and car rental costs \(\pounds 150\) per week.
Driving out costs \(\pounds 900\) for ferries, road tolls, fuel and overnight expenses.
  1. Draw a decision tree to model this situation. Advise Jane on the cheapest option. As an alternative Jane considers buying a car to keep at the house. This is a long-term alternative, and she decides to cost it over 10 years. She has to cost the purchase of the car and her flights, and compare this with the other two options. In her costing exercise she decides that she will not be tied to two trips per year nor to four trips per year, but to model this as a random process in which she is equally likely to do either.
  2. Draw a decision tree to model this situation. Advise Jane on how much she could spend on a car using the EMV criterion.
  3. Explain what is meant by "the EMV criterion" and state an alternative approach.
Question 2:
AnswerMarks Guidance
214 28
21 1 
Question 2:

2 | 14 | 28 | 15 | 27
2 | 1 | 1 | 3 | 3
2 Jane has a house on a Mediterranean island. She spends eight weeks a year there, either visiting twice for four weeks each trip or four times for two weeks each trip. Jane is wondering whether it is best for her to fly out and rent a car, or to drive out.\\
Flights cost $\pounds 500$ return and car rental costs $\pounds 150$ per week.\\
Driving out costs $\pounds 900$ for ferries, road tolls, fuel and overnight expenses.\\
(i) Draw a decision tree to model this situation. Advise Jane on the cheapest option.

As an alternative Jane considers buying a car to keep at the house. This is a long-term alternative, and she decides to cost it over 10 years. She has to cost the purchase of the car and her flights, and compare this with the other two options.

In her costing exercise she decides that she will not be tied to two trips per year nor to four trips per year, but to model this as a random process in which she is equally likely to do either.\\
(ii) Draw a decision tree to model this situation. Advise Jane on how much she could spend on a car using the EMV criterion.\\
(iii) Explain what is meant by "the EMV criterion" and state an alternative approach.

\hfill \mbox{\textit{OCR MEI D2 2008 Q2 [16]}}
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Q1 16 Q2 16 Q3 20 Q4 20