P = number of professors

P_i = the i_th professor, where i=1..P

C = number of classes to be offered

C_j = the j_th class, where j=1..C

S_i = { C_k | k in [1..C], where C_k can be taught by P_i }

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Unknown:

T_i = The time slot for the i_th class

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Constraint:

Mutual Exclusion ... to be filled in ...