Chhaya owns a software company that has a research budget of 350,000 euros. She is considering investing part of this budget into the development of a new antivirus software. The development of the new software requires an upfront investment of 50,000 euros. After this investment is made, the development will succeed or fail with equal probability. If the development succeeds, Chhaya will have to decide between licensing the new software to another company or marketing it herself. She estimates that she can license it for 100,000 euros. If she chooses to market it herself, her profit from the software will depend on the economic conditions. She will make a profit of 300,000 euros if the economy is up and incur a loss of 100,000 euros if the economy is down. The economy will be up with probability 0.75 and down with probability 0.25. The success of the development phase and the economic conditions are independent. If Chhaya decides not to invest in the development, the research budget remains the same. Chhaya's primary concern in this context is to maximize the expected monetary value. a. (20 PTS) Draw a decision tree to represent this problem. Clearly label all nodes and include all relevant information. Find the optimal strategy and the maximum expected monetary value. b. (15 PTS) State the optimal strategy if there is perfect information that will resolve all the uncertainties at once (i.e., perfect information that will tell what will happen at every chance node) and determine the expected value of this perfect information. C. (15 PTS) Suppose licensing is not an option and perform two-way sensitivity analysis of Chhaya's problem (the original version without information) with respect to the probability p that the development will be successful and the probability 9 that the economy will be up