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EX 242 present (b) Before the decision is made, the results of a long-term forecast become avale able. These suggest that demand will continue to rise at the Estimates of the reliability of this forecast are given below: P(forecast predicts demand increasing at current rate when actual demand will rise at faster rate) = 0.3 when actual demand will continue to rise at the current rate) = 0.7 p(forecast predicts demand increasing at current rate p(forecast predicts demand increasing at current rate when Determine whether the company should, in the light of the forecast, change (c) Discuss the limitations of the analysis you have applied above and suggest (6) The managers of a soft drinks company are planning their production strategy ways in which these limitations could be overcome. actual demand will rise at a slower rate or fall) = 0.4 from the decision you advised in (a). for next summer . The demand for their products is closely linked to the weather and an analysis of weather records suggests the following probability distribu tion for the June to August period: Weather conditions Probability Hot and dry Mixed Cold and wet 0.3 0.5 0.2 1.0 The table below shows the estimated profits ($000s) which will accrue for the different production strategies and weather conditions: Weather conditions Production strategy Hot and dry Mixed Cold and wet Plan for high sales Plan for medium sales Plan for low sales 400 200 110 100 180 100 -100 70 90 pany's marketing manager estimates that there is a 0.3 probability that aver- EXERC 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 (a) On the basis of the information given, determine: (ii) The expected value of perfect information. (i) The course of action which will maximize expected profits. Discuss the practical implications of your result. (b) A long-range weather forecast suggests that next summer's weather condi- tions will, in general, be cold and wet. The reliability of the forecast is indi- cated by the following probabilities which are based on past performance: of a new car-cleaning product. For simplicity, the potential average sales of the product during its lifetime are classified as being either high, medium or low timated to be $80 million, $15 million and -$40 million, respectively. The com- age sales will be high, a 0.4 probability that they will be medium and a 0.3 w 243 In the light of the long-range weather forecast, should the company chang 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 How much would it be worth paying for the information from the test? Assume that the company's objective is to maximize expected profit.) 18. The managers of Red Valley Auto Products are considering the national launch indication