5 is the value obtained by adding only the latter half after the branch, as in Screen layout (3) + Screen input/output items (2) = 5 (picking up the 5 person-days of Report list in the table gives the same number). It does not include the preceding task Screen list (4 person-days) in the path, and moreover this lower path itself is not the longest one, so it cannot be the number of days on the critical path.
×Incorrectイ
9 is the lower path, Screen list (4) + Screen layout (3) + Screen input/output items (2) = 9 days, and the calculation of that path itself is correct. However, the critical path means the longest path, so as long as the 10-day upper path exists, 9 days cannot be the answer. The correct reading is that this lower path has 10-9=1 day of slack (float).
○ウ
正解Looking at the arrow diagram, the screen-design tasks branch into two after “Screen list” and merge again at the end node. There are two paths from start to finish. The upper one is Screen list (4 person-days) → Screen flow (6 person-days), giving 4+6=10 days. The lower one is Screen list (4 person-days) → Screen layout (3 person-days) → Screen input/output items (2 person-days), giving 4+3+2=9 days. The critical path is the path with the longest duration among all paths from start to finish, so comparing 10 days with 9 days, the longer one, 10 days, is the number of work days on the critical path of screen design. As for the people in charge, Screen flow is Tanaka while Screen layout and Screen input/output items are Suzuki, so they are different people; together with the note “There are no persons in charge with the same surname”, the two paths can proceed in parallel. Therefore the correct answer is ウ, 10.
×Incorrectエ
15 is the value obtained by simply summing the effort of the four screen-design tasks: 4+6+3+2=15. However, Screen flow and Screen layout → Screen input/output items branch after Screen list, and different people in charge can carry them out in parallel. This is the number of days if everything were performed serially, which contradicts the order relationships shown in the figure, so it is wrong.
ここがポイント
The critical path is the path with the longest duration among all paths from start to finish on an arrow diagram (PERT chart), and its length is the shortest possible duration for the whole project. It is neither the simple sum of all effort nor the shortest path.
Branched tasks can be carried out in parallel, so at a merge point you take the maximum of the durations of the paths reaching it. Paths other than the longest one have slack (float), while a delay in a task on the critical path delays the whole project.