A manager is trying to form a team of four members (not including herself) using Belbin's Team Roles. According to the Belbin model, there are nine team roles which can be categorized as ACTION-ORIENTED, PEOPLE-ORIENTED, and THOUGHT-ORIENTED. - The ACTION-ORIENTED team roles are Shaper, Implementer, and Finisher. - The PEOPLE-ORIENTED team roles are Coordinator, Worker, and Investigator. - The THOUGHT-ORIENTED team roles are Plant, Monitor, and Specialist. The manager must choose the team members from seven employees. Each employee has a preference for each of the nine team roles ranging from 0 (least preferred) to 100 (most preferred) as shown in the table below. (A Microsoft Excel file of the table can be downloaded here) For example, Employee 1 has the highest preference to be a Plant (89) and the lowest preference to be an Implementer (2). Also, for the Shaper role, Employee 7 has the highest preference (91) and Employee 5 has the lowest preference (3). The manager would like to maximize the total satisfaction of the team (summation of all team member preferences from their assigned roles) with the following conditions. 1. There must be four members in the team. 2. At least one team member must fulfill an ACTION-ORIENTED role. 3. At least one team member must fulfill a PEOPLE-ORIENTED role. 4. At least one team member must fulfill a THOUGHT-ORIENTED role. 5. Each team member can fulfill only one role. 6. Each team role can be fulfilled by more than one member. 7. Not all team roles need to be fulfilled. Use integer programming to determine which employees should be part of the manager's team and what role should each one fulfill.