Question

Dr. Maureen Becker, the head administrator at Jefferson County Regional Hospital, must deter- mine a schedule for nurses to make sure there are enough of them on duty throughout the day. During the day, the demand for nurses varies. Maureen has broken the day into twelve 2-hour periods. The slowest time of the day encompasses the three periods from 12:00 a.m. to 6:00 a.m., which, beginning at midnight, require a minimum of 35, 15, and 25 nurses, respectively. The demand for nurses steadily increases during the next four daytime periods. Beginning with the 6:00 a.m.-8:00 a.m. period, a minimum of 35, 60, 80, and 90 nurses are required for these four periods, respectively. After 2:00 p.m. the demand for nurses decreases during the afternoon and evening hours. For the five 2-hour periods beginning at 2:00 p.m. and ending at midnight, 70, 65, 60, 45, and 30 nurses are required, respectively. A full-time nurse reports for duty at the beginning of one of the 2-hour periods and works 8 consecutive hours (which is required in the nurses' contract) and paid at a rate of $30/hr. A part-time nurse reports for duty at the beginning of one of the 2-hour periods and works 4 consecutive hours (which is required in the nurses' contract) and paid at a rate of $18/hr. At each shift, the number of full-time nurses must be greater than or equal to the number of part-time nurses. Dr. Becker wants to determine a nursing schedule that will meet the hospital's minimum requirements throughout the day while using the minimum labor cost. a. (10 points) Formulate a linear programming model for this problem. (Define the decision variables and formulate the objective function and constraints).