Assembly times and fatigue. A company is considering having the employees on its assembly line work 4 10-hour days instead of 5 8-hour days. Management is concerned that the effect of fatigue as a result of longer afternoons of work might increase assembly times to an unsatisfactory level.
An experiment with the 4-day week is planned in which time studies will be conducted on some of the workers during the afternoons. It is believed that an adequate model of the relationship between assembly time, y, and time since lunch, x, should allow for the average assembly time to decrease for a while after lunch before it starts to increase as the workers become tired.
Write a model relating E(y) and x that would reflect the management's belief, and sketch the hypothesized shape of the model.