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Exercises 175
(11) In the Eagle Mountain Forest controlled fires are used for a number
of purposes. These include enhancing wildlife habitat by eliminating
decadent vegetation and clearing ground for planting seedlings.
The planning and carrying out of a controlled fire involves the
advanced commitment of a large amount of resources, but weather
conditions at the time of the fire mean that there is no guarantee
it will be successful. For example, under certain conditions the
quality of the burn may be poor, and additional resources will need
to be employed to achieve the objectives. At worst, the fire can
‘escape’. If this happens the losses of additional forest and the extra
resources involved in bringing the fire under control will amount
to an estimated cost of $40 000.
The managers of the forest want to apply burning to a 14 acre
area of forest near Saltern Lake. If the burn is successful the
benefits of the operation are estimated to be worth $10 000. The
managers have to choose between ‘conventional burning’ and
‘yarding’. Conventional burning would cost an estimated $4000.
Yarding involves using a bulldozer to remove large material from
the forest before using fire. This reduces the difficulty of controlling
the fire, but costs an additional $200 per acre.
If either type of treatment is used the fire will either be successful,
or there will be problems with the quality of the burn or the fire will
escape. For a conventional burn these probabilities are estimated
to be 0.848, 0.150 and 0.002, respectively. If yarding is used these
probabilities are estimated to be 0.899, 0.100 and 0.001. If there are
problems with the quality of the burn the forest managers will have
to decide whether to extinguish the fire at a cost of $1000 or whether
to apply $2000 worth of additional resources which will give them
a 0.8 probability of achieving all of the benefits, a 0.1 probability of
achieving benefits worth $3000 and a 0.1 probability of achieving
no benefits.
If the managers wish to maximize the expected net benefits (i.e.
benefits–costs) of the operation, determine their optimum policy.
(12) A local council owns an underground railway system and the
railway’s managers have to make a decision on whether to lower
fares in an attempt to increase passenger numbers. If they decide
to reduce fares they will then have to decide whether to launch an
advertising campaign on local television to increase awareness of
the fare reduction. If fares remain the same then it is estimated that
there is a 0.7 probability that the mean number of passengers carried
per day over the next year will equal 20 000 and a 0.3 probability