A large city is experiencing problems with waste treatment. The ThrowMe&Co company is planning to begin recycling newspapers, aluminium cans, and plastic containers in this city and may opt to create a large recycling factory, or a small one. A large factory would need an initial investment of AUD60,000, while a small one AUD30,000. The profit of the initiative depends on the proportion of households that get to participate. The city has 1.5 million households as potential recyclers. After conducting initial analysis, ThrowMe&Co determined that for every 1000 households that participate in their program, the contribution to profit will be AUD800. It is believed that 50 000, 150 000, 250 000, or 350 000 households will participate, with probabilities 0.1, 0.35, 0.30 and 0.25 respectively. ThrowMe&Co can, at a price of AUD10,000, request a consultancy report, to study the potential reaction of households to their program. The report will be for strong reaction of households or for weak reaction of households with probabilities 0.4 and 0.6 respectively. If the report predicts strong reaction, then the chances for 50 000, 150 000, 250 000, or 350 000 households to be involved are 0.1, 0.1, 0.4 and 0.4. If the report predicts weak reaction, then the chances to involve 50 000, 150 000, 250 000, or 350 000 households are 0.4, 0.2, 0.25 and 0.15 respectively. Conduct the following: a) Represent the situation as a decision tree and give clear description of the possible states of nature, outcomes and policies on the tree. b) Use the analytical form [arctg(x-50/50)-arctg(-1.6)]/[arctg(3.2)-arctg(-1.6)] to calculate the utility over the monetary outcomes in the decision problem. c) Solve the decision tree according to the principle of maximum expected utility. Clearly show your steps in solving the decision tree. d) Discuss the results from the utility analysis and the recommended policy in light of the problem at hand.