Kaguta, an experienced project manager for a construction project was struggling to bring back to life a building that had stalled for some years due to scarcity of funds. He provided the following information regarding the said project.

Activity	Normal time (weeks)	Crash time (weeks)	Normal cost (Kshs)	Crash cost (Kshs)
1-2	10	7	1000	1600
1-3	15	11	2000	2800
2-4	8	6	1800	2600
2-5	-	-	-	-
3-5	20	16	4500	5700
3-6	28	23	7200	9700
4-5	14	12	5000	6000
5-6	12	9	3300	4500

Required;

(i) Draw the network diagram for the project, identify the critical path and completion time based on the normal times. (6 marks)

(ii) Identify all the paths for the project. (2 marks)

(iii) Determine the minimum project completion time with the least cost increase over normal costs and draw the new network diagram. (6 marks)