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.

The following distances and two-way flows are given:

	DISTANCES BETWEEN OFFICES (FEET)
	1	2	3	4	5	6	7	8
1		10	25	34	15	18	20	30
2			18	25	18	15	10	20
3				10	20	10	15	18
4					30	20	18	15
5						10	25	34
6							18	25
7								10
8

	TWO-WAY FLOWS (UNITS PER PERIOD)
	A	B	C	D	E	F	G	H
A		4	0	0	6	0	0	0
B			0	0	0	3	0	3
C				0	0	0	0	3
D					2	0	0	0
E						4	0	0
F							2	0
G								3
H

a. If there are no restrictions (constraints) on the assignment of professors to offices, how many alternative assignments are there to evaluate?

multiple choice

40,320

64

1,024

25,600

64,000

There are an infinite number of possibilities

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. How many possible solutions (assignments of faculty to offices) satisfy all of the stated constraints?

c. Suppose the biology department has selected the following final layout:

A-1	B-2	G-3	H-4
COURTYARD
E-5	F-6	C-7	D-8

What is the total flow-distance cost measure of this solution?