This question's explanation and your answers so far.
ある機械の組立て作業のメンバになった P さんは，リーダの指導の下，作業工程を確認するためにアローダイアグラムを作成した。作成したアローダイアグラムは，効率よく作業を進行させるために，メンバ間で共有することにした。図 1 にアローダイアグラムを示す。 各工程は 1 人で行うものとして計画し，メンバの誰が担当しても予定日数で作業を終了するものとする。 図1のEの時点で, この組立て作業の納期を短縮する必要が発生し, 他の作業を担当していたQさんが2日間, このプロジェクトの工程を手伝ってくれることになった。 プロジェクトを早期に終了させるためには, どの工程をどれだけ手伝ってもらうのがよいか。
Process 7 is on the via-F path (6 days) and is not on this section's critical path, via G (8 days). Shortening a non-critical process does not change the total number of days (= the critical path), so it has no shortening effect.
正解 In the section after E in Figure 1 (E→H) there are three paths: via F (process 7 + process 8 = 4 + 2 = 6 days), direct (process 9 = 6 days), and via G (process 10 + process 11 = 4 + 4 = 8 days). The total number of days for the whole project is determined by the longest path (the critical path), so unless you shorten the longest one in this section, via G = 8 days, the whole will not shrink. If Q helps with process 10 for 2 days, process 10 goes from 4 days to 2 days, and via G becomes 2 + 4 = 6 days, matching the other two paths (both 6 days). This makes E→H go from 8 days to 6 days, shortening the whole by 2 days. The difference from the other paths is 8 - 6 = 2 days, and Q's 2 days exactly matches this limit of shortening, so choice イ, concentrating 2 days on process 10, is optimal.
Both process 7 and process 8 are on the via-F path (6 days) and are not on the critical path, via G. Even if both are shortened, via F merely becomes 4 days; the longest, via G at 8 days, is unchanged, so the total number of days is not shortened.
Process 7 is on the via-F path and process 9 is on the direct path; neither is on the critical path, via G. Even if they are shortened, the longest, via G at 8 days, is unchanged, so the total number of days is not shortened.