This question's explanation and your answers so far.
電化製品を製造している G 社では，新たに開発した製品 H の発売を予定しており，その製造方法及び販売計画について検討を行っている。 製品 H の製造方法として案 A と案 B の二つの案が検討されていて，それぞれの案の固定費と変動費は表1のようになると見込んでいる。 表1 案Aと案Bの固定費と変動費の見込額
| 固定費（万円／月） | 変動費（万円／台） | |
|---|---|---|
| 案A | 1,400 | 6 |
| 案B | 2,000 | 5 |
製品 H の月当たり製造台数と，固定費と変動費を合計した製造原価の関係は，図1のグラフのように表すことができる。 図1 製造台数と製造原価の関係（横軸＝製造台数，縦軸＝製造原価（万円）。製造台数 0 のとき案Aは 1,400 万円，案Bは 2,000 万円から始まり，案Aの直線の傾きが案Bより大きいため，両者は途中で交差し，それより右側では案Bが案Aより下になる。） 案Aと案Bのどちらで製品Hの製造原価が低くなるのかは，製品Hの製造台数によって異なる。案Bの製造原価が案Aの製造原価より低くなるのは，月間製造台数が何台を超える場合か。
At n＝120, plan A ＝ 1,400＋6×120＝2,120 and plan B ＝ 2,000＋5×120＝2,600 (10,000 yen), so plan B is 480 (10,000 yen) more expensive. In Figure 1 this is still well to the left of the crossing point, in the range where plan A with its smaller fixed cost is advantageous. Dividing the difference in fixed cost, 600, not by the difference in variable cost of 1 per unit but by plan B's variable cost of 5 per unit gives 120, so this is the value you get when you divide by the wrong quantity.
At n＝300, plan A ＝ 1,400＋6×300＝3,200 and plan B ＝ 2,000＋5×300＝3,500 (10,000 yen), so plan B is still 300 (10,000 yen) more expensive. In Figure 1 it has not yet reached the 600 units where the two lines cross; it is merely an intermediate number of units where the plan B line is still above the plan A line.
At n＝400, plan A ＝ 1,400＋6×400＝3,800 and plan B ＝ 2,000＋5×400＝4,000 (10,000 yen). The gap has narrowed to 200 (10,000 yen), but plan B is still higher and the order has not reversed yet. Choosing this because the gap is shrinking is a hasty mistake. The reversal happens only after 600 units, where the gap becomes zero.
正解 Manufacturing cost ＝ fixed cost ＋ variable cost × number of units manufactured. So if the monthly number of units manufactured is n, plan A is 1,400＋6n (10,000 yen) and plan B is 2,000＋5n (10,000 yen). The condition for plan B to be cheaper is 2,000＋5n ＜ 1,400＋6n. Rearranging both sides gives 2,000－1,400 ＜ 6n－5n, that is 600 ＜ n, so plan B becomes advantageous once n exceeds 600 units. This is the same as the calculation “difference in fixed cost 600 (10,000 yen) ÷ difference in variable cost per unit 1 (10,000 yen per unit) ＝ 600 units”, and it corresponds to the point where the two lines cross in Figure 1. Indeed, at n＝600, plan A ＝ 1,400＋6×600＝5,000 and plan B ＝ 2,000＋5×600＝5,000 (10,000 yen), exactly equal; at n＝601, plan A ＝ 5,006 and plan B ＝ 5,005 (10,000 yen), so plan B is lower. Therefore the correct answer is エ, 600.