1. Consider a model of the post office as a third-order material delay (equation (1 1-4)). Assume that the mailing rate is constant and that the system is in equilibrium- the mailing rate and delivery rate are equal. Without using simulation, sketch the behavior you expect if the delay time suddenly and permanently increases from 5days to 10 days on day5. Make two graphs-one showing the mailing rate and delivery rate and the other showing what you expect to happen to the stock of letters in transit. Sketch the response you would expect if the delay time suddenly dropped from5to2.5days.

Outflow = DELAYn(Inflow, D): Total Material in Transit = Material in Transit, i=1 Material in Transit, = INTEGRAL(Net Inflows, Material in Transit,(0)) Material in Transit (0) = Inflow * D Inflow - Exit Rate Stage, fori = 1 Net Inflow rate, = Exit Rate Stage; - Exit Rate Stage, fori E (2, . . .,n - 1) Exit Rate Stage,-, - Outflow fori = 1 Exit Rate Stage, = Material in Transit /(D) forie (1, . . .,n - 1) Outflow = Material in Transit /(D) (11-4)