Teaching Period Period Period Period Period Period Period Period Period Period Assistant 1 2 3 4 5 E Iamp; E 9 10 E_---___E-I-E-E-

An academic department chair wants to assign teaching assistants to the sections of a large lecture. The sections are held in 5 periods on Monday and 5 periods on Tuesday. The periods are numbered from 1 to 10. All teaching assistants are available for the 10 periods but they have preferences about the different periods. The following table shows these preferences represented as a value between 1 and 3 where 1 indicates lowest preference and 3 indicates highest preference. For example, if a teaching assistance prefers to teach period 1 then the value for that would be 3, if she is neutral about it, her preference value would be 2, and if it is her least preference, then the value would be 1. Develop an integer programming model to maximize satisfaction of teaching assistance preferences given that each of them must work 2 periods during those two days .