This question's explanation and your answers so far.
組立生産される製品W，X，Y，Zの1個当たりの利益，1個当たりの組立作業時間，組立作業1分当たりの利益，1週間の最大生産可能数は表のとおりである。1週間の利益を最大にするように生産計画を立てるとき，製品Zの生産個数は幾つか。ここで，1週間の総組立作業時間は40時間であり，製品W，X，Y，Zの全てを生産する必要はなく，同時には一つの製品しか組立生産できないものとする。
| 1個当たりの利益 A（千円） | 1個当たりの組立作業時間 B（分） | 組立作業1分当たりの利益 C=A/B（千円／分） | 1週間の最大生産可能数 D（個） | |
|---|---|---|---|---|
| 製品W | 50 | 20 | 2.5 | 40 |
| 製品X | 60 | 40 | 1.5 | 50 |
| 製品Y | 90 | 30 | 3 | 20 |
| 製品Z | 100 | 50 | 2 | 45 |
0 units is the case of not producing Z at all, but Z's profit per minute C=2 is higher than X's 1.5, so after finishing Y and W, using the remaining time on the more cost-effective Z maximizes profit. The remaining 1000 minutes can be used for Z, so it is not 0 units; this is wrong.
There is no basis corresponding to 8 units (8×50 min = 400 min). After producing Y and W up to their limits, 1000 minutes remain, and Z can be produced in 20 units. 8 units is a value obtained by miscalculating the remaining time or the production limit, so it is wrong.
正解 The constraint is a total assembly work time of 40 hours = 2400 minutes. Since only one product can be assembled at a time and it is not necessary to produce every product, the best way to get the maximum profit from the limited time is to give priority to the products with the larger “profit per minute of assembly work C=A/B” and allocate each up to its limit. In descending order of C: Y (3) → W (2.5) → Z (2) → X (1.5). First producing Y up to its limit of 20 units (20×30 min = 600 min), then W up to its limit of 40 units (40×20 min = 800 min) uses 1400 minutes in total, leaving 2400−1400 = 1000 minutes. Next, allocating the remaining 1000 minutes to Z, which has the next-highest C, gives 1000÷50 = 20 units (fewer than the limit of 45, so all can be allocated), exactly using up the remaining time. There is no time left for X, which has the lowest C. Therefore the number of units of product Z produced is 20, and choice ウ is correct.
45 units is Z's maximum producible quantity per week D, but producing 45 units requires 45×50 = 2250 minutes, and the 1000 minutes left after prioritizing Y and W are not enough. This is the mistake of jumping to the conclusion that it can be produced up to the limit.