An Introduction to Management Science 13th Edition by David Anderson,Dennis Sweeney ,Thomas Williams ,Jeffrey Camm, Kipp Martin

Exercise 22

The Delta Group is a management consulting firm specializing in the health care industry. A team is being formed to study possible new markets, and a linear programming model has been developed for selecting team members. However, one constraint the president imposed is that the team size should be three, five, or seven members. The staff cannot figure out how to incorporate this requirement in the model. The current model requires that team members be selected from three departments and uses the following variable definitions:
x 1 5 the number of employees selected from department 1
x 2 5 the number of employees selected from department 2
x 3 5 the number of employees selected from department 3
Show the staff how to write constraints that will ensure that the team will consist of three, five, or seven employees. The following integer variables should be helpful: