Suppose that three general surgeons share a single operating room (OR) dedicated to their surgical department. Surgeon a needs to perform surgeries indexed by 1, 2, 3 and 4; surgeon b performs surgeries 5 and 6; surgeon c performs surgery 7. Due to surgeon preferences, the following precedence relationships must be considered for the surgeries of surgeons a and b while creating the OR schedule for a particular day. Note that it is not necessary for a surgeon to complete all of her surgeries in her list before another surgeon starts working on her surgeries. The scheduler needs to sequence these 7 surgeries with the objective of minimizing the total weighted completion time. Note that and values for surgeries =1,2,3,4,5,6,7 are given below. Based on the below parameter values, find all optimal sequences.

1 2 3 4 5 6 7 surgeries W; P; 1 18 12 8 8 17 16 3 6 6 5 4 8 9