※ Our check while writing this explanation could not fully confirm the published answer; scoring follows IPA's official key.
×Incorrectア
7 comes from applying the 70% limit to the wrong quantity. If you take the leftover 10 that could not be allocated for the 10:00 normal order after the limit of 70 was applied — or if you mistakenly think the stock is 10 — and multiply it by 0.7, you get 10×0.7=7. The actual stock at 11:00 is 20, so the quantity being multiplied is wrong and this value is incorrect.
×Incorrectイ
10 is obtained by allocating the full 80 for the 10:00 normal order without applying the 70% limit and then computing the remaining stock as 100−80−10=10. This both ignores the rule in item (2) of the passage that a normal order can be allocated only up to 70% of the stock quantity, and answers the remaining stock rather than the allocatable quantity that the question asks for, so it is wrong on two counts.
○ウ
正解Inventory allocation is processed in order of order time, from earliest to latest, and the upper-limit rule for each order type is applied to the stock quantity at that point in time. The given starting stock is 100.
(1) 10:00, normal order of 80 — a normal order can be allocated up to 70% of the stock quantity. 100×0.7=70, so only 70 can be allocated against the order of 80. The remaining 10 must wait for the next stock arrival. The stock becomes 100−70=30.
(2) 10:30, priority order of 10 — a priority order can be allocated up to the full stock quantity. Since stock 30 ≧ 10, all 10 are allocated. The stock becomes 30−10=20.
(3) 11:00, normal order of 40 — the stock at this point is 20, and because this is a normal order the limit is 20×0.7=14. Since 14 is smaller than the order quantity of 40, the quantity that can be allocated is 14.
Therefore the answer is ウ, 14. There are two key points: the 70% limit applies to the stock quantity at the time of processing, not to the order quantity; and the stock decreases by the amount that has been allocated.
×Incorrectエ
20 is simply the stock quantity at 11:00 itself. If the order were a priority order, which can be allocated up to the full stock quantity, then 20 would be the answer; but the 11:00 order is a normal order, whose limit is restricted to 70% of the stock. Overlooking the difference in limits between order types leads to this choice.
ここがポイント
The allocation limit differs by order type: a normal order is limited to the stock quantity at that point in time × 70%, and a priority order is limited to the stock quantity at that point in time. The limit is calculated from the stock quantity, not from the order quantity.
Multiple orders are processed in order of order time from earliest to latest, and the stock decreases by the quantity allocated. The limit for a later order must be recalculated based on the reduced stock quantity.