BUSA2020 Exam Revision Questions
Question 1
The table below contains information on 500 users of yPhones from manufacturer PineApple:
Claimant Age Group
Adolescent Adult Elderly Total
Sydney 50 120 20 190
City of Sale Melbourne 40 150 5 195
Brisbane 30 55 30 115
120 325 55 500
You may assume that each user is a different person.
PineApple would like to use this demographics data to predict future demographics.
Q1) What proportion of users are from Melbourne?
Q2) what proportion of users are EITHER:
• Adults living in Melbourne, or
• Elderly, but not living in Melbourne?
Q3) A randomly selected user is found to be an adult. What is the chance that this user doesn’t
live in Sydney?
Q4) What is the probability that a randomly selected user will neither be from Brisbane, nor elderly?
1
Question 2
Let X, Y , and Z be three events in a sample space S, as shown below:
X Y
Z
S
For each of the events listed below, clearly shade in the corresponding part of the Venn diagram.
X ∪ Z Y C ∩ Z
(X ∪ Y )C ∩ Z X ∪ (Y ∩ Z)
2
Question 3
BUSA Airlines is a small company that only operates flights between Sydney and Melbourne. A
standard practice in the airline industry is to only fill planes with the minimal required amount of
fuel necessary to save on costs.
BUSA is analysing a particular flight from Sydney to Melbourne, and has hired you to build a model
to estimate the price they should be charging for this flight. For simplicity, assume each passenger
will be charged the same price.
Here are some key facts BUSA has provided you:
• The number of passengers taking this flight depends only on the price BUSA decides to charge.
• BUSA assumes each passenger weighs 80kg (on average).
• Each passenger is allowed exactly 30kg of luggage. BUSA assumes that each passenger takes
exactly this amount.
• BUSA will need to staff the flight with the same number of crew members and equipment,
regardless of the number of passengers.
The total weight of the flight will depend on these three factors, and in turn, determine the minimum
amount of fuel needed for the flight.
Ultimately, BUSA Airlines is looking to choose a price P that will maximise their profit for this
flight. Their costs will come from the amount of fuel they need to use, as well as wages and other
costs for their crew and equipment. The revenue will come solely from ticket sales (this is not the
case in practice, but we will ignore this detail).
Q1) State and clearly label the decision variable(s) and parameters for the model.
Q2) Draw an influence diagram for the information described above. HINT: Your diagram should
include the following nodes:
• Ticket Price
• Number of Passengers
• Baggage weight per Passenger
• Individual Passenger weight
• Total Baggage Weight
• Total Passenger Weight
• Total Weight of the Flight
• Crew and Equipment
• Fuel
• Total Costs
• Revenue
• Profit
Q3) Suppose a spreadsheet model has been built for the scenario described. How might BUSA
Airlines use the model to find the optimal price that maximises profit?
3
Question 4
Mega Media is a marketing company that designs custom marketing campaigns for its clients. They
have a simple operating structure that categorises all client projects into small or large projects.
Small projects are fairly easy to come by, and on average it takes the sales team half a day of work
to source a client for a small project. Large projects take much more work for the sales team. On
average, it will take 3 full days to source a client for a large project.
Once a project is sourced by the sales team, it is handed to the design team to create and deliver
the marketing campaign. Small projects take 50 work-hours to complete, whereas large projects take
150 hours to complete.
Mega Media would like to set a target for the number of small and large projects it should target
over the next year. They intend to only accept a project if they can be reasonably sure they can
complete it so that they maintain their great reputation with their clients.
Mega Media’s sales team effectively works for 240 days each year (after taking into account peak
and off-peak business times, annual and other leave, time taken to train new staff, etc.). The design
team, however, is a bit larger and can work a total of 18,000 work-hours over the next year.
After costs, the profit for each small project on average is $6,000, and the profit for each large project
is $25,000. Whilst Mega Media is must maintain their reputation, they still want to maximise their
profits while doing so.
Let S be the number of small projects and L be the number of large projects that Mega Media will
target over the next year.
Q1) State the objective function.
Q2) State the constraint functions (in addition to S ≥ 0 and L ≥ 0).
Q3) Sketch and clearly label the feasible region. Clearly label the constraint functions using their
equations.
Q4) By checking the extreme points of the feasible region, determine the optimal solution to the