This question's explanation and your answers so far.
A工場では，製品Xを生産している。今週金曜日に受注した大口注文に対応するために，翌週できるだけ多く生産することにした。次の条件で生産するとき，翌週金曜日の終業時に出荷可能となる製品Xは何台か。ここで，各日の部品在庫数，製品Xの製造台数及び出荷可能台数は表のとおりである。 〔条件〕 ・製品Xの生産台数は，1日に最大12台である。 ・今週金曜日に製品Xの60台分の部品を発注し，発注した部品は，翌週金曜日の始業時に納品される。 ・他の注文に対する出荷は無いものとする。 ・製造上の不良品は発生しない。
| 曜日 | 今週 金 | 翌週 月 | 翌週 火 | 翌週 水 | 翌週 木 | 翌週 金 |
|---|---|---|---|---|---|---|
| 始業時の部品在庫数（製品Xの製造台数に換算） | 55 | 45 | ||||
| 当日の製品Xの製造台数 | 10 | 12 | ||||
| 終業時の製品Xの出荷可能台数 | 15 | 27 |
注記 網掛けの部分は，表示していない。
57 is the total number of units made from Monday through Friday of next week (12+12+12+9+12=57). But what is asked is how many units of product X are shippable at the end of business next Friday, and as the table shows, 15 units are already in a shippable state at the end of business this Friday. Since there are no shipments for other orders, those 15 units carry over as they are, giving 57+15=72 units. Counting only what is produced next week and forgetting to add the existing stock leaves you with 57.
60 is the number of shippable units at the end of business next Thursday, that is, the value you get by leaving out a whole day of production on next Friday. The conditions state that the parts for the 60 ordered units are delivered at the start of business next Friday, so on Friday those parts can be used to produce on that same day. Reading the delivery as arriving at the end of business and treating Friday as having zero production leaves the value at 60. Also, the order quantity itself is exactly 60 units worth, so it is easy to be pulled by that number among the choices and answer with the order quantity itself.
正解 The correct answer is ウ “72”. The starting point is to read two rules out of the table. First, the parts inventory: this Friday starts with 55 and 10 units are made that day, while next Monday starts with 45, so “inventory at the start of the next day = inventory at the start of the day − units made that day”; in other words, each unit of product X consumes one unit worth of parts. Second, the shippable units: the 15 at the end of business this Friday plus the 12 units made on Monday gives exactly the 27 at the end of business on Monday, so “shippable units at the end of a day = shippable units at the end of the previous day + units made that day”, and because there are no shipments for other orders (a stated condition), everything produced simply piles up. After that, since the factory produces as much as possible, it makes the daily maximum of 12 units as long as parts remain, and you only have to fill in the shaded cells of the table day by day. Next Tuesday starts with 33 parts, so 12 units are made and the shippable total is 27+12=39; Wednesday starts with 21, makes 12 units, for 51; Thursday starts with only 9 units worth of parts, so it cannot reach the limit of 12 and makes only 9 units, for 60, at which point the parts inventory becomes 0. Next Friday, the parts for the 60 ordered units are delivered at the start of business and the inventory recovers to 60, but the daily production limit is 12 units, so only 12 can be made, and the shippable total at the end of business is 60+12=72 units. The key to this question is that the parts constraint (Thursday) and the production-capacity constraint (Friday) become bottlenecks on different days.
75 is the value obtained by assuming that the maximum of 12 units can be made on all five days from Monday through Friday of next week (15+12×5=75). In reality only 9 units worth of parts remain at the start of business on Thursday, and no additional delivery arrives before the start of business on Friday, so Thursday can produce only 9 units, not 12. Looking only at the daily production-capacity limit without checking the material-side constraint of the parts inventory overcounts by 3 units and gives 75.