Q1. The personnel director of a hospital is trying to decide how many orderlies to hire and train for the next four months. According to admissions forecasts, the demand for orderly-hours for the next four months is: Union requirement ask for a guaranteed 37.5 hours work week, with overtime prohibited to maintain a high employment level. This implies each employed orderly is paid for 150 hours a month. Hospital records indicate 10% of the orderlies quit their jobs each month. Orderlies are given a 1-month training period; hence they must be hired a month before being assigned regular duty. They are paid $400 a month while in training and $900 a month afterward. It takes approximately 10 hours of regular orderly time to train each trainee during the training period; that is, the number of hours available for regular service by orderlies is reduced by 10 for each trainee. Currently six orderlies are available. No one will be laid off; each orderly will work a few hours less, but be paid for full employment. Formulate a linear program to solve the personnel director's staffing problem. (10 marks)