2. A risk-neutral art gallery is deciding whether to invest in renovating its very old building with fire-resistant materials to fully protect its artwork from fire damage. The renovation work would cost $200,000. If the renovation is undertaken, the cost of damage resulting from any subsequent fire is known to be $0. If the renovation is not undertaken, the probability of fire is assumed to be T = 0.0035. In the event of a fire (without renovation work), the cost of damage to artwork will depend on how quickly firefighters arrive. If firefighters arrive quickly (with a probability of 0.75), the cost of damage would be $25 million, but if they do not arrive quickly (with a probability of 0.25) the cost of damage would be $150 million. Ignore insurance considerations for parts (a) and (b). (a) Draw the decision tree for this problem and use it to determine whether the art gallery should undertake the renovation work. (b) Other things equar i. how sensitive is the decision in (a) to the probability of fire if renovation is not undertaken (i.e. sensitivity to the 0.0035 value)? i. how sensitive is the decision in (a) to the probability of firefighters arriving quickly (i.e. sensitivity to the 0.75 value)? (c) Discuss whether it is reasonable to assume a 'risk-neutral' art gallery. Note no calculations are required here