Nurse staff scheduling (Khan and Lewis [1987]). To provide adequate medical service to its constituents at a reasonable cost, hospital administrators must constantly seek ways to hold staff levels as low as possible while maintaining sufficient staffing to provide satisfactory levels of health care. An urban hospital has three departments: the emergency room (department 1), the neonatal intensive care nursery (department 2), and the orthopedics (department 3). The hospital has three work shifts, each with different levels of necessary staffing for nurses. The hospital would like to identify the minimum number of nurses required to meet the following three constraints:

(1) the hospital must allocate at least 13, 32, and 22 nurses to the three departments (over all shifts);

(2) the hospital must assign at least 26, 24, and 19 nurses to the three shifts (over all departments); and

(3) the minimum and maximum number of nurses allocated to each department in a specific shift must satisfy the following limits:

Suggest a method using maximum flows to identify the minimum number of nurses required to satisfy all the constraints.