Mass Mart, a large department store, has a very successful and profitable package wrapping department. The department uses two complex bow-making machines that work inline to make the bows for the packages. There is one skilled operator who knows how to operate the machines. She had been very reliable, but recently has had increasing health problems which caused her to miss work about 10 percent of the time. Bow-making Machine 1 has a reliability of 0.97. Machine 2 has a reliability of 0.90.

a. What is the current reliability of the system, including the operator?

b. Management is considering either scrapping Machine 2 and replacing it with a new machine which has a reliability of 0.97 at a cost of $5,000, or training another operator to fill in when the first operator is absent at a cost of $5,100. The prospective trainee has an excellent attendance record and has only been absent 4 days out of 250 work days for the department, last year. Management estimates that profits from the department would increase by $6,000 per year, if the bow-making line operated at 100 percent of capacity. If management wants to pay off its investment in the first year, determine the expected net profit for each alternative, and recommend which one will be the most profitable to management.