A municipality is evaluating three different alternatives for city water filtration system. Details of each alternative is given below: Alternative A: The project requires $400,000 investment in year n=0 and it has an annual operating cost of $60,000. This alternative has a useful life of 7 years. Alternative B: The project requires $300,000 in investment in year n=0 and it has an operating cost of $65,000 per year. This alternative has a total useful life of 13 years. Alternative C: The project requires $350,000 investment in year n=0. The operating cost for the project is $38,000 in year n=1 and increases by 5% each year until the end of its useful life of 10 years. For all there alternatives, there are no salvage values and annual social benefit is estimated to be $150,000 per year. We know that the social discount rate is 15% per year. a) (10 points) Calculate the profitability index (P I) for all three alternatives separately. b) (15 points) Using the profitability index (P I) analysis, find the most attractive alternative given that the required service period is infinite and each alternative can be repeated with the same financial attributes. Show your work clearly to obtain full credit. (Hint: you are comparing mutually exclusive alternatives with unequal service lives)