Schwartz Transport owns a lorry with a one-year old engine. It has to decide whether or not to replace the engine at a cost of ‚¬2,000. If it does not replace the engine, there is an increased chance that it will break down during the year and the cost of an emergency replacement is ‚¬3,200. Then at the end of next year, the company again has to decide whether to replace the engine or not. When an engine is replaced any time during the year, it is assumed to be one year old at the end of the year. The probabilities that an engine breaks down during the next year are as follows:

Draw a decision tree for this problem, and find the decisions that minimise the total cost over the next two years. If a three-year-old engine is virtually certain to break down sometime in the next year, what is the minimum expected cost over threeyears?

Age of engine Probability of breakdown . 0.2 0.7