A project requires an investment of $1000 now in a machine and will generate $x 0 at the end of the first year, $100 at the end of the second year increasing thereafter by $50 each year compared to the preceding year with the last revenue occurring at the end of the 10th year from now. The machine then broke down and was sold two years after the last revenue for a salvage value of $300. Consider a minimum attractive rate of return (MARR) of 20% per year.

(a) Use Descartes or Norstroms test to determine the possible number of solutions for the rate of return (ROR) of this project. (5 points)

(b) Suppose x = 0. Find the rate of return (ROR) and show that the project is not profitable. (5 points)

(c) Suppose x > 0. Find the minimum value for x which would make the project profitable. (15 points)