The managers of a soft drinks company are planning their production strategy for next summer. The demand for their products is closely linked to the weather, and an analysis of weather records suggests the following probability distribution for the June to August period:
The table below shows the estimated profits ($000s) which will accrue for the different production strategies and weather conditions:
(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)?