This question's explanation and your answers so far.
次の条件で，製品Xを製造する。部品Y，部品Zの歩留りが表のとおりであるとき，製品Xを300個製造するために必要な部品Yの原材料投入量aは何kgか。ここで，製品Xの歩留りは100%で，部品は全て新規に製造するものとする。 〔製品Xの製造条件〕 ・1個の組立て製品Xは，3個の部品Y及び1個の部品Zで構成されている。 ・部品Y及び部品Zは，それぞれの原材料から製造して用いる。 ・部品Y及び部品Zは，原材料1kgから1個製造することができる。
| 部品種類 | 原材料投入量 | 歩留り | 部品の完成数 |
|---|---|---|---|
| Y | a kg | 90% | |
| Z | 600 kg | 50% | 300個 |
注記 網掛けの部分は，表示していない。
225 is far below the 900 finished units required. Since 1 kg of raw material makes 1 unit and the yield is 90% (less than 100%), the input can never be smaller than the number of completed units. With 225 kg you would obtain only 225×0.9 = 202.5 finished units, nowhere near 900.
250 is likewise smaller than the required 900 finished units, so it cannot hold. An input of 250 kg produces only 250×0.9 = 225 finished units. This value is easy to choose if you mistake the requirement as just 1 unit of part Y for each of the 300 units of product X, or if you pay no attention to the size relationship between the input and the number of completed units.
900 is “the number of finished units of part Y required”, not “the raw material input”. It is the value obtained by treating the yield as 100% (that is, forgetting to divide by 90%). If the yield is 90%, the input must always exceed the number of completed units; with 900 kg you obtain only 900×0.9 = 810 finished units, which means 30 units of product X cannot be made.
正解 What we must find is “the raw material input a for part Y”. Think of it in two steps. First, find how many finished units of part Y are needed. One product X consists of 3 units of part Y and 1 unit of part Z, and the yield of product X is 100%, so 300 units of product X require exactly 3×300 = 900 finished units of part Y. Next, work backward from the yield. Part Y can be manufactured as 1 unit from 1 kg of raw material, so an input of a kg puts a units into production, but since the yield is 90%, only a×0.9 units are actually usable. Therefore a×0.9 = 900, so a = 900÷0.9 = 1,000 kg. The row for part Z in the table, 600 kg×50% = 300 units, matches the given condition exactly, which also confirms that the relationship “input × yield = number of completed units” is correct. Hence the correct answer is エ, 1,000.