Task 1
A manufacturing company introduces two product alternatives. The table below provides profit
payoffs in thousands of dollars.

The probabilities for the state of nature are P(Up) = 0.35, P(Stable) = 0.35, and P(Down) = 0.30.

1) Use a decision tree to recommend a decision with justification.
[3 Marks]

2) Use the expected value of perfect information (EVPI) to determine whether the
manufacturing company should attempt to obtain a better estimate of the response.
Justify your answers.
[3 Marks]

3) A test market study of the potential demand for the product is expected to report either
a favourable (F) or unfavourable (U) condition. The relevant conditional probabilities are
as follows:
P(F|Up) = 0.5; P(F|Stable) = 0.3; P(F|Down) = 0.2
P(U|Up) = 0.2; P(U|Stable) = 0.3; P(U|Down) = 0.5
Use Bayes’ theorem to compute the conditional probability of the demand being up,
stable, or down, given each market research outcome. Justify your answers.

[4 Marks]
Task 2
You are required to formulate a research problem in a field and use multiple linear regression
technique to model the chosen problem. The potential fields are relevant to, but are not limited
to, the following:
• Logistics management
• Supply chain management
• Warehousing management
• International trade
• Transport management
• Business policy and regulations

Analyse the chosen problem through completing the following tasks:

1) Clearly state the formulated research problem and explain its background and significance.
(Word limit: 100)
[2 Marks]
2) Determine the potential dependent and independent variables (at least one categorical
and two quantitative independent variables). Justify the choice of variables. (Word limit:
100)
[3 Marks]
3) Collect real data for the chosen variables with the minimum sample size of 30 and perform
the multiple linear regression model in Excel.
[2 Marks]
4) Interpret the estimation result in terms of R^2, F-test, and individual t-tests.
[3 Marks]

Task 3
A soft drink manufacturing company has three factories—one in Orlando, one in Tampa, and one
in Port St. Lucie—which supply soft drink bottles to three warehouses located in the city of Miami
(W1, W2 and W3). The associated per-unit transportation cost table is provided below.
The factory in Orlando has a manufacturing capacity of 15,000 units.
The factory in Tampa has a manufacturing capacity of 18,000 units.
The factory in Port St. Lucie has a manufacturing capacity of 8,000 units.
The requirements of the warehouses are:
1) Determine how many of each company’s production should be shipped from its factory
to each warehouse in order to minimise the total transportation cost? Justify your findings.
[5 Marks]
2) Find an alternative optimal solution for this transportation problem? Justify your findin