QBUS6820: Prescriptive Analytics Assignment 1 Semester 1, 2024
Instructions: Submit your answers in one pdf document with each question/part labelled clearly. You
must also submit your code - the raw code (.ipynb file) and a html version of your Jupyter Notebook.
Problem 1: Investing (6 marks)
Suppose a friend of yours wants to invest $10,000 and has asked for your help. They’re thinking of
investing in an index fund tied to the ASX200 and a tech stock fund, but they’re concerned about
the volatility of tech stocks. They therefore want to take measures to manage their investment risk.
They’ve decided that the amount invested in the tech fund cannot be higher than twice the amount
invested in the index fund. The price per share of the index fund is $17, and the price per share of
the tech fund is $20. Over the last 5 years, the average annual return for the index fund has been
15%, and 25% for the tech fund. They expect the performance of the funds in the coming year to be
identical to the recent past. Your friend wants to develop an investment strategy that will maximise
their return for the coming year.
(a) Formulate a linear programming model to help determine how much money they should invest
in each fund.
(b) Solve the model using Python.
(c) If your friend can get $1 more to invest, how will that affect the solution? $2 more? $3 more?
What can you say about the return on their investment strategy given these changes.
Problem 2: Producing wine (7 marks)
A winery produces and sells three types of wine across Australia — No.1, No.2, and No.3. A few
months ago management discovered a large number of grapevines in the vineyard were infested with
an insect pest that feeds on their roots and eventually kills them. They had no choice but to take
out all the grapevines and replant their crop. It will take years for the new vines to mature and
produce grapes so in the meantime they must purchase grape juice from other vineyards to make
their wine.
There are three vineyards that are willing to sell their grape juice to the company - A, B, and C.
They are located in different and faraway parts of the country. As such, the company is looking
at using more conveniently located winemaking and bottling facilities instead of its own. It has
identified 4 facilities: W, X, Y, and Z.
In a particular month vineyard A can supply 1,500 tons of grape juice, vineyard B 1,600 tons, and
vineyard C 1,000 tons. The processing capacity per month at facility W is 1,300 tons, 1,000 tons at
X, 1,300 tons at Y, and 1,500 tons at Z. The $ cost per ton of transporting juice from the vineyards
to the facilities is as follows:
W X Y Z
A 850 720 910 750
B 970 790 1,050 880
C 900 830 780 820
The processing facilities have different equipment and have different wage rates. The cost of processing each type of wine at each plant ($/ton) therefore differs, and is as follows:
W X Y Z
No.1 2,100 2,350 2,200 1,900
No.2 4,100 4,300 3,950 3,900
No.3 2,600 2,300 2,500 2,800
This month the company needs to process a total of 1,400 tons of No.1, 800 tons of No.2, and 600
tons of No.3 at the four facilities combined. There are two complicating factors though. To produce
1 ton of No.2 requires 2 tons of grape juice, and 1 ton of No.3 requires 1.5 tons of grape juice. 1 ton
of No.1 requires 1 ton of juice.
The company wants to know how many tons of grape juice to ship from each of the vineyards to each
of the facilities, and the number of tons of each type of wine to produce at each facility to minimise
total costs.
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QBUS6820: Prescriptive Analytics Assignment 1 Semester 1, 2024
Problem 3: Assigning groups (7 marks)
Assume you’re a course coordinator assigning 15 students to 5 teams for a project. You want the
project teams to be relatively equal in terms of academic performance and to have a mix of different
skills and domestic/international students. You’ve decided to use students’ grade point average
(GPA) as a proxy for academic performance and to set a minimum average GPA of 2.75 for each
team while also maximising the overall average GPA across teams. You’ve also decided to use
students’ majors as a proxy for different skill sets, but you don’t want there to be more than two of
the same major in any single team. You also want at least one international student on each team,
but not more than two. The following table details the GPA, major, and internationality of each
student in the cohort.
Student GPA International Major
1 3.10 Yes FIN
2 2.30 No ACCT
3 2.31 Yes BA
4 2.10 Yes MKTG
5 3.28 No BA
6 3.90 No FIN
7 2.92 No FIN
8 2.60 No FIN
9 3.17 No FIN
10 3.03 Yes MKTG
11 3.40 Yes MKTG
12 2.73 No ACCT
13 2.66 Yes MKTG
14 2.86 No ACCT
15 3.40 Yes BA
Formulate and solve an integer linear programming model for this problem to determine project
teams that align with your criteria. Do you think your model does a decent job of making sure the
teams are diverse and academically equitable? If not, how might you change your model to achieve
a better result?
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