An automated transfer line is to be designed. Based on previous experience, the average downtime per occurrence = 5.0 min, and the probability of a station failure that leads to a downtime occurrence p = 0.01. The total work content time = 9.8 min and is to be divided evenly amongst the workstations, so that the ideal cycle time for each station = 9.8/n. Determine
(a) the optimum number of stations on the line n that will maximize production rate, and
(b) the production rate and proportion uptime for your answer to part (a).