a) Draw a decision tree for this problem, including all relevant data. b) Using expected values, analyse the decision tree and recommend one option, with reasons:
As a result of an increase in demand for a town’s car parking facilities, the owners of
a car park are reviewing their business operations. A decision has to be made now
to select one of the following three options for the next year:
Option 1 : Make no change. Annual profit is RM150, 000. There is little
likelihood that this will provoke new competition this year.
Option 2 : Raise prices by 50%. If this occurs there is a 75% chance that an
entrepreneur will set up in competition this year. The Board’s
estimate of its annual profit in this situation would be as follows:
2A WITH new competitor 2B WITHOUT new competitor
Probability Profit (RM) Probability Profit (RM)
0.3 200, 000 0.5 250, 000
0.4 170, 000 0.3 200, 000
0.3 130, 000 0.2 150, 000
Option 3 : Expand the car park quickly, at a cost of RM50, 000, keeping prices
the same. The profits are then estimated to be like 2B, above, except
that the probabilities would be 0.6, 0.3 and 0.1 respectively.
Required
a) Draw a decision tree for this problem, including all relevant data.
b) Using expected values, analyse the decision tree and recommend one option,
with reasons:
c) State any assumptions or reservations in your analysis.
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