A large manufacturing company has had a very difficult time for the last couple of years in the market it operates. Its Board of Directors must now decide whether or not a new factory should be built and the size of the factory. The MD of the company suggests that the company should conduct a market survey to gauge how the market will react to the product that the company intends launching. The research department has provided the following information: P (favourable selling conditions) = 0.55P(favourable market research/favourable selling conditions) = 0.75P(unfavourable market research/unfavourable selling conditions) = 0.80It is estimated that a large factory under favourable selling conditions will realize a profit of $300000, but will suffer a loss of $200000 under unfavourable selling conditions. In addition, it is estimated that a small factory will realize a profit of $200000 if selling conditions are favourable, but will suffer a loss of $120000 under unfavourable selling conditions. The cost of conducting market research will amount to $10000, which is not taken into account when calculating profit and loss. With the aid of a labeled decision tree, determine the optimal course of action the company should take. Show details of your calculations.