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240 Revising judgments in the light of new information
Weather conditions
Production strategy Hot and dry Mixed Cold and wet
Plan for high sales 400 100 −100
Plan for medium sales 200 180 70
Plan for low sales 110 100 90
(a) On the basis of the information given, determine:
(i) The course of action which will maximize expected profits;
(ii) The expected value of perfect information
and discuss the practical implications of your result.
(b) A long-range weather forecast suggests that next summer’s
weather conditions will, in general, be cold and wet. The reliability
of the forecast is indicated by the following probabilities
which are based on past performance:
p(cold, wet conditions forecast when weather will be hot
and dry) = 0.3
p(cold, wet conditions forecast when weather will be
mixed) = 0.4
p(cold, wet conditions forecast when weather will be cold
and wet) = 0.6
In the light of the long-range weather forecast, should the
company change from the course of action you recommended
in (a)?
(7) A company has just received some ‘state of the art’ electronic
equipment from an overseas supplier. The packaging has been
damaged during delivery and the company must decide whether
to accept the equipment. If the equipment itself has not been
damaged, it could be sold for a profit of $10 000. However, if the
batch is accepted and it turns out to be damaged, a loss of −$5000
will be made. Rejection of the equipment will lead to no change
in the company’s profit. After a cursory inspection, the company’s
engineer estimates that there is a 60% chance that the equipment
has not been damaged. The company has another option. The
equipment could be tested by a local specialist company. Their test,
however, is not perfectly reliable and has only an 80% chance of
giving a correct indication.
How much would it be worth paying for the information from
the test? (Assume that the company’s objective is to maximize
expected profit.)