Question B5
[15 marks]
Phalaborwa Development Corporation, PDC, purchased land that will be a site of a new luxury
double storey complex. The location provides a spectacular view of the surrounding countryside,
including mountains and rivers. PDC plans to price the individual units between R300 000 and R1 400
000.
PDC commissioned preliminary architectural drawings for three different projects; one with 30 units,
one with 60 units and one with 90 units. The financial success of the project depends upon the size
of the complex and the chance event concerning the demand of the units.
The statement of the decision problem is to select the size of the new complex that will lead to the
largest profit given the uncertainty concerning the demand of for the units.
The information for the PDC case (in terms of action and states of nature), including the
corresponding payoffs can be summarised as follows:
States of Nature
Strong Demand (s_1)
0.8
Demand (s_2)
0.2
Probability
Decision Alternative
Small Complex (d_1)
8
7
Medium Complex (d_2)
14
5
Large Complex (d_3)
20
-9
The management of PDC is considering a six month market research study designed to learn more
about the potential market’s acceptance of the PDC project. Management anticipates that the
market research study will provide the following two results:
(1) Favourable report: A significant number of the individuals contacted express interest in
purchasing a PDC unit
(2) Unfavourable report: very few individuals contacted express interest in purchasing a PDC
unit.
If the market study is undertaken
P(Favourable report) = 0.77
P(Unfavourable report) = 0.23
If the market report is favourable
P(strong demand given favourable report) = 0.94
P(weak demand given favourable report) = 0.06
If the market report is unfavourable
P(strong demand given unfavourable report) = 0.35
P(weak demand given an unfavourable report) = 0.65.