With 300,000 yen you cannot cover all three essential measures (Task 2, Task 3, and Task 4). For example, avoiding only Task 2 and Task 3 while leaving Task 4 alone gives 5+30+12 = 47 days, and avoiding only Task 4 and Task 1 (5+25 = 300,000 yen) gives 5+(18+17)+10 = 50 days; both exceed 45 days. The cost is the smallest, but it does not satisfy the condition, so it is not acceptable.
○イ
正解First, check Figure 1, the arrow diagram for the software development (Figure 1 is the shared figure of the multi-part question that starts at Q89, and it is printed on a page before this question). The arcs are: 1→(preparation task, 5 days)→2, 2→(Task 1, 20 days)→4, 2→(Task 2, 15 days)→3, 3→(Task 3, 15 days)→4, 4→(Task 4, 10 days)→5. Path 1→2→4→5 takes 5+20+10 = 35 days, and path 1→2→3→4→5 takes 5+15+15+10 = 45 days. The critical path is therefore preparation task → Task 2 → Task 3 → Task 4, and the shortest number of days for finishing on schedule is 45 days. Under the condition that these 45 days must be kept, judge one by one which avoidance measures are essential. First, every path passes through Task 4, so its +2-day delay pushes the whole project out by 2 days; avoiding it is essential, at a cost of 50,000 yen. Next, while keeping Task 4 at 10 days, staying within 45 days requires 5 + (the longest stretch from node 2 to node 4) + 10 ≤ 45, that is, both Task 1 and Task 2 + Task 3 must be 30 days or less. Task 2 + Task 3 is exactly 15+15 = 30 days with no delay, so if even one of them slips, it goes over 30 days. Therefore avoiding Task 2 (150,000 yen) and Task 3 (150,000 yen) is also essential. Task 1, on the other hand, is not on the critical path and has 10 days of slack (float); even with a +5-day delay it is 20+5 = 25 days ≤ 30 days, so there is no need to spend money to avoid it. The minimum required cost is thus 5+15+15 = 350,000 yen, that is 35 in units of 10,000 yen, and the correct answer is イ.
×Incorrectウ
450,000 yen is the amount you get when you drop one of the essential measures for Task 2 or Task 3 and instead buy the unnecessary measure for Task 1 (250,000 yen) — for example Task 1 + Task 3 + Task 4 = 25+15+5, or Task 1 + Task 2 + Task 4 = 25+15+5 (in units of 10,000 yen). Task 1 is a non-critical task with 10 days of float, and even a +5-day delay does not affect the overall duration, so the 250,000 yen is wasted. Moreover, the delay of the dropped Task 2 (+3 days) or Task 3 (+2 days) makes the critical path 48 days or 47 days, so the 45-day condition is not met either.
×Incorrectエ
600,000 yen is the total when all four avoidance measures are implemented (25+15+15+5 in units of 10,000 yen). It does keep the project within 45 days, but it spends 250,000 yen even on Task 1, which has slack, so it is not the minimum. The question asks for the smallest cost that satisfies the condition, so 350,000 yen is the appropriate answer.
ここがポイント
In an arrow diagram, you compare the durations of all paths; the longest path is the critical path, and it determines the shortest completion time. In this question it is 45 days (preparation task → Task 2 → Task 3 → Task 4).
A delay in a task on the critical path directly affects the overall duration, so an avoidance measure is essential; but for a non-critical task that has spare days (float), no measure is needed as long as the delay stays within that float. Making this distinction is the key to finding the minimum cost.