Read the following case study based on the Applegold Cider Company. You should then apply decision analysis to the problem facing Apple gold. This will involve: a) Formulating the problem

as a decision tree; b) using Bayesian analysis to update prior probabilities and find the correct probabilities in the tree; c) discuss the strengths and limitations of your analysis. Applegold is a major cider producer, producing draught cider for pubs and clubs,as well as bottles and cans, which has recently seen production and the number of outlets selling its products increase significantly.The growth in draught cider has created some problems for the company's managers.In particular, there is concern that when sales reach their peak in August, there might not be enough kegs (steel re-usable cider containers) available to meet demand.Apple gold own about 200000 kegs, but it is felt by some managers that the stocks should be increased.The Operations Manager has proposed that 16000 new kegs be ordered immediately. The Accountant is not convinced. Kegs cost £90 each, so this would lead to an expenditure of £1440000. They would be usable next year, but assuming 5%interest on capital, buying now rather than waiting would cost £72000. 4The Sales Manager proposes that the company wait until an accurate long range weather forecast is available for August, since demand depends heavily on the weather, with hot dry months leading to high demand. Such a forecast will be available in July. One problem is that it might be the case that other brewers had bought all of the available kegs by this time and the Operations Manager estimates a probability of 0.7 of getting the kegs if they wait until July.The Sales Manager produces an interim forecast, with no knowledge of the weather,of how good sales are likely to be in August. She estimates that they will be at least 10% higher with probability 0.45, they will increase by a lower amount with probability 0.4, and there will be no increase with probability 0.15.The Data Processing Manager suggests three possible strategies; buying 0, 8000 or16000 kegs immediately. The associated change in profit from these three strategies were estimated, based upon the assumption that with a 10% sales increase 16000extra kegs will be used (if available), and for a lower increase 8000 extra kegs will be used (if available), with an associated profit of £10.50 per keg. These are summarised in Table 1. Table 1: Predicted changes in profit (in £) for combinations of different immediate purchasing strategies and sales increases.The Sales Manager suggests that it might still be better to wait for the weather forecast in July, and run the risk of the kegs not being available. Whether it is best to do so depends upon how accurate the forecasts are.