問41
頻出度★★★
生産性が同じメンバ5名で20日掛かる作業がある。作業開始直前に3名がインフルエンザにかかったので新たなメンバと交代させることにした。新メンバの生産性は当初予定していたメンバの60%の生産性であるとき，20日以下で作業を完了するためには，少なくとも何名の新メンバが必要か。
平成23年度 特別試験 ITパスポート試験 問41
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This question's explanation and your answers so far.
解説
問 41
Incorrectア
With 4 new members the capacity is not enough. The equivalent capacity is only 2 + 4 × 0.6 = 4.4, so the work would take 100 person-days ÷ 4.4 ≈ 22.7 days. That exceeds the 20-day deadline, so it does not work. Thinking that the same number as the 3 who dropped out, or one more than that, is enough means failing to account for the fact that the new members have only 60% productivity.
- イ
正解 The key to this question is to measure the whole workload in person-days. The original plan was 5 members of equal productivity working for 20 days, so the total workload is 5 members × 20 days = 100 person-days. Three members dropped out with influenza, so 5 − 3 = 2 of the original members remain. In 20 days these 2 members can finish 2 × 20 = 40 person-days. Therefore the amount the new members must cover within 20 days is 100 − 40 = 60 person-days. Each new member's productivity is 60% of an original member's, so one new member working 20 days produces 0.6 × 20 = 12 person-days. Letting n be the number of members needed, 12n ≥ 60 gives n ≥ 5, so the minimum is 5 members. Checking with the daily capacity gives the same result. The 2 remaining original members plus 5 new members give an equivalent capacity of 2 + 5 × 0.6 = 5.0, which restores exactly the capacity of the original 5 members. 100 person-days ÷ 5.0 = exactly 20 days, which satisfies the condition of 20 days or fewer. Therefore the correct answer is イ, 5.
Incorrectウ
With 7 new members the work does finish within 20 days (equivalent capacity 2 + 7 × 0.6 = 6.2, 100 ÷ 6.2 ≈ 16.1 days), but what the question asks is at least how many, that is, the minimum number required. Since 5 members make it in exactly 20 days, 7 is more than necessary and is not the minimum.
Incorrectエ
With 9 new members the equivalent capacity is 2 + 9 × 0.6 = 7.4 and the work finishes in 100 ÷ 7.4 ≈ 13.5 days, but this is not the minimum number required either. If you mistakenly calculate as if the new members had to carry the whole 100 person-days of work on their own (100 ÷ 12 ≈ 8.3 → 9 members), you leave out the 40 person-days contributed by the 2 remaining original members, and that is how this value comes out.
ここがポイント
- The basis of effort calculation is to grasp the workload as a fixed quantity using number of people × duration = person-days (effort). First fix the total of 5 members × 20 days = 100 person-days, then break it down into how many person-days each side covers.
- When members with different productivity are mixed together, convert each into the equivalent number of standard members and add them up. One member with 60% productivity counts as 0.6 of a standard member, so the capacity of the 2 remaining members plus n new members can be written as 2 + 0.6n.
- When the question asks at least how many, answer with the smallest integer that satisfies the condition (here, 20 days or fewer). Even if several options satisfy the condition, only the smallest one is the correct answer.
用語