The Question about Decision Theory.

Please write step by step and clearly. Thanks a lot^u^

Prolessor Plum is getting tired of being accused of murder and wants to develop a security system for the Tudor mansion. He is writing a proposal to the Boddy Foundation Trust for a 5250,000 grant, Plum reckons that it will cost his department 50,000 to prepare a proposal with a 50% chance of winning the bid. However, his PhD students, Watson and Sherlock, are uncertain how they will turn Prolessor Plum's wacky ideas into a working security system if he gets the award. Plum came up with three braliant' ideas. - The first is to recreate 'The Machine', an artificialy intelligent mass surveillance system created by Finch. Plum forgets to mention that Finch is a fictional character in a TV show and now the students have to try to create 'The Machine' for 50,000, with a probability of 0.5 of being successitul. - The second is to terive Skynet, yet another fictional mass survediance system. The students think they can reprogram Skynet for co0,000, with a 70% chance of success. - The third solution involves buying a license from the Oracle and acquiring a few Agents from the Archtect. It will cost them E120,000, with certain success. Protessor Plum only has lab space to work on one approach at a time, and only has time to try two of the three approaches. However, if a first attempt tails, his second choice must be the Orade license (if he is awarded the grant in the first place, of course). (a) Represent this decision problem by a decision tree, including all relevant details. Solve this decision problem: explain what Prolessor Plum should do and give the mopected money value (EMV) of your suggested course of action. [Professor Plum's first decision is whother or not to prepare the proposal. If he chooses not to do so, the process ends with payoff zero. If the grant proposal is not successful, the process onds with payott - E50,000.1 (b) Present the risk protile of the optimal solution for this decision problem and verity the EMV corresponding to the optimal decision. Discuss this risk protie. (c) Suppose that it is possible to got pertect information with regard to whether or not Protessor Plum's proposal will get the contract. What would be the expected value of this information, and what is the maximum you would recommend Plum to pay for this intormation? To what change in the decision tree does this correspond? HOUEWOAK. OECISKCN TREES (d) Suppose that, before deciding whether to put in a proposal, it is possible to pertorm detailed research that will reveal, without error, whether or not the first idea to implement 'The Machine' will be successful, What is the expected vale of this information and the maximum you would recommend Professor Plum to pay for it? To what change in the decision tree does this coirespond? Consider a similar scenario to the above. except that now this opportunity exists for the Skynet rerival. Again, find the expected value of this intormation and the maximum price Plum should pay for in. To what change in the decision tree does this correspond? (e) What would you recommend as the maximum price to pay for perfect intormation about all of the uncertainties in the pecblem together? To what change in the decision tree does this correspond