In production flow-shop problems, performance is often evaluated by minimum makespan, this being the total elapsed time from starting the first job on the first machine until the last job is completed on the last machine. We might expect that minimum makespan would be linearly related, at least approximately, to the number of jobs. Consider the following data, with X denoting the number of jobs and Y denoting the minimum makes pan in hours:
(a) From the standpoint of engineering economics, what would a nonlinear relationship signify?
(b) What does a scatter plot of the data suggest about the relationship?
(c) If appropriate, fit a simple linear regression model to the data and estimate the increase in the minimum makespan for each additional job. If doing this would be inappropriate, explain why.