A company purchased a machine (defender) 2 years ago for $50,000. The machine has a current market value of $25,000. Although the machine has a remaining useful life of 3 more years, it can be replaced with a new one (challenger) which will cost $60,000 and has a useful life of 3 years. The estimated market values and operating & maintenance costs of both machines for the next 3 years of service are shown in the table given below. Defender Challenger Year MV O&M MV O&M 1 $20,000 $24,000 $50,000 $18,000 2 $15,000 $26,000 $45,000 $23,000 3 $10,000 $30,000 $40,000 $29,000 The company's before-tax MARR is 10%. (a) What is the economic service life of the challenger? Explain your answers and state the major assumptions made. (6 marks) (b) If the study period is infinity, when should the company replace the defender with the challenger? Explain your answers and state the major assumptions made. (8 marks) (c) What is the Present Worth of the cost for the optimal replacement plan in part (b)? (3 marks) (d) If the study period is 2 years, what is the optimal replacement plan for the company and its Present Worth of cost? (8 marks)