Project which is about to start consists of activities listed below:-Activity Immediate Predecessor Duration

A None 4 B A 13 C A 5 D C 11 E C 3 F D, E 4 G None 3 H A, G 5 I G 4 J H 17 K H 2 L J, K 3 M F, L 3 N B, M 3 O L, M 2 P O 3 Q N, P 4

The project should be completed by the end of week 38. If the project is delayed beyond this date, it estimated that it will cost the firm Kshs. 30,000 a week

i) Draw a network to represent the project and determine the critical path.

ii) What is the earliest time at which the project can be completed and what penalty cost, if any, will be incurred?

iii) Activity K is a two-week course to train new salesmen. The hotel which will be used for the course has been booked for weeks 12 and 13. In the light of your analysis, should this booking be change

  i) see below

  ii) end of week 41; 90,000 penalty

  iii) no change required

Explanation:

i) There appear to be two separate "no predecessor" tasks: A and G. There appear to be two separate "no successor" tasks: I and Q. A representation of the network is shown below. The pink bar across the middle is the critical path.

The pink task K is shown as fixed, dependent upon the hotel booking (see part iii).

Where starts or ends line up, a dependency is implied. Where there is some ambiguity in that regard, the specific dependency is shown with a letter.

In general, tasks are shown with the latest possible start. (K is an exception.) Slack time is shown with a dash.

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ii) The critical path has a length of 41 weeks. That is 3 weeks longer than the required duration, so a penalty of 3×30,000 = 90,000 is expected.

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iii) Activity K can start as early as week 10 or as late as week 25. There is no need to change the hotel booking for weeks 12 and 13.