The Dorton University president has asked the OSCM department to assign eight biology professors (A, B, C, D, E, F, G, and H) to eight offices (numbered 1 to 8 in the diagram) in the new biology building.

a. If there are no restrictions (constraints) on the assignment of professors to offices, how many alternative assignments are there to evaluate?
b. The biology department has sent the following information and requests to the OSCM department:
Offices 1, 4, 5, and 8 are the only offices with windows.
A must be assigned Office 1.
D and E, the biology department co- chairpeople, must have windows.
H must be directly across the courtyard from D.
A, G, and H must be in the same wing.
F must not be next to D or G or directly across from G.
Find the optimal assignment of professors to offices that meets all the requests of the biology department and minimizes total material handling cost. You may use the path flow list as a computationalaid.

PATH FLOW A-B 2 A-C 0 A-D 0 A-E5 A-F 0 A-G 0 A-H 0 PATH FLOW PATH FLOW PATH FLOW PATH FLOW B-D 0 B-E 0 B-F 3 B-G 0 B-H 2 C-D 0 C-E 0 C-F 0 C-G 0 C-H 3 DE 4 D-F 0 D-G 0 D-H 0 E-F 1 E-G 0 E-H 0 F-G 1 F-H 0 G-H 4