Read the following case study based on the Applegold Cider Company. You should

then apply decision analysis to the problem facing Applegold. 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.

Applegold own about $100000$ kegs, but it is felt by some managers that the stock

sholud be increased.

The Operations Manager has propoased that $8000$ new kegs be ordered immediately.

The Accountant was not convinced. Kegs cost $60$ each, so this would lead to an

expenditure of $480000.$ They would be usable next year, but assuming $5\%$ interest

on capital, buying now rather than waiting until next year would cost $24000.$