(1) Consider a scenario where a hospital has to allocate six nurses (from a pool of ten) to three different departments: Emergency Room (ER), Intensive Care Unit (ICU), and Pediatrics. Each department needs at least two nurses, but the total number of nurses for each department should not exceed three. Each nurse has a different effectiveness score for each department as shown in the table below. Nurse 1 234567 7 8 560 9 10 Emergency Room Intensive Care Unit Pediatrics 7.1 7.9 7.3 8.1 8.5 00 00 00 00 8.9 8.7 8.1 8.4 8.2 10 001 8.4 8.2 8.3 8.9 7777778777 -57TSO 10 40 00 7.8 7.5 7.7 7.4 7.6 8.0 7.6 7.5 7.8 7 00 00 00 00 00 8.4 7.5 12 21 8.2 7.5 8.2 8.0 1 7.8 Formulate an integer programming problem to inform a selection that maximises the total score attained by the nurses. You do not have to solve the model, but define all decision variables in your model unambiguously and provide explanatory comments for model constraints.