Question

the following gives task duration for software project activities. what is the minimum number of days to finish this project? task duration (days) dependencies t1 8 t2 6 t1 t3 10 t1, t2 t4 7 t3 t5 12 t2, t3 t6 15 t4, t5

Answer 1

Explanation:

To calculate the minimum number of days required to finish this project, we need to use the critical path method (CPM), which involves identifying the longest sequence of dependent tasks and their durations.

First, we need to draw the network diagram for the project:

```

|---(T1-8)---(T3-10)---|

(T2-6) (T5-12)

| / |

|---(T4-7)---(T6-15)---|

```

Next, we need to calculate the earliest start time (EST), earliest finish time (EFT), latest start time (LST), and latest finish time (LFT) for each task. For the starting task, EST = 0 and EFT = 0.

```

EST EFT LST LFT

T1 (8 days) 0 8 22 30

T2 (6 days) 0 6 6 12

T3 (10 days) 8 18 22 32

T4 (7 days) 18 25 25 32

T5 (12 days) 18 30 32 44

T6 (15 days) 32 47 32 47

```

The critical path is the longest sequence of dependent tasks that have no slack (i.e., the difference between LST and EST, or LFT and EFT, is zero). In this case, the critical path is T1-T3-T5-T6.

Therefore, the minimum number of days to finish this project is the sum of the durations of tasks on the critical path:

8 + 10 + 12 + 15 = 45 days

Therefore, the minimum number of days required to finish this project is 45 days.