Norton Industries is installing a new computer system. The activities, the activity times, and the project network are as follows.

Activity	Time
A	3
B	6
C	2
D	5
E	4
F	3
G	9
H	3

A project network is given with the starting point on the left and the ending finish point on the right with activities A through H. The arcs between the activities are listed as follows.

• Start to A and B
• A to C
• B to D and G
• C to D and G
• D to E
• E to F
• F and G to H
• H to Finish

The critical path calculation shows B-D-E-F-H is the critical path, and the expected project completion time is 21 weeks. After viewing this information, management requested overtime be used to complete the project in 16 weeks. Thus, crashing of the project is necessary. The following information is relevant.

	Time (weeks)	Cost ($)
Activity	Normal	Crash	Normal	Crash
A	3	1	900	1,700
B	6	3	2,000	4,100
C	2	1	500	1,000
D	5	3	1,800	2,400
E	4	3	1,500	1,850
F	3	1	3,000	3,900
G	9	4	8,000	9,800
H	3	2	1,000	2,000

(a)Formulate a linear programming model that can be used to make the crashing decisions for this project. (The objective function should be the additional cost of crashing. Let

x_i=

the finish time for activityiand

y_i=

the amount of time activityiis crashed wherei= A, B, C, D, E, F, G, and H.)Min

s.t.constraint A

constraint B

C depends on A

D depends on C

D depends on B

E depends on D

F depends on E

G depends on C

G depends on B

H depends on G

H depends on F

finish time for H

maximum crashing for A

maximum crashing for B

maximum crashing for C

maximum crashing for D

maximum crashing for E

maximum crashing for F

maximum crashing for G

maximum crashing for H