This question's explanation and your answers so far.
問91
頻出度★★★
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
※ Our check while writing this explanation could not fully confirm the published answer; scoring follows IPA's official key.
×Incorrectア
At 135,000 yen, sales revenue is 135,000 yen × 400 units = 54,000,000 yen, and subtracting the cost of sales of 38,000,000 yen leaves a gross profit of only 16,000,000 yen — 4,000,000 yen short of the 20,000,000 yen target. This price is too low to satisfy the condition.
○イ
正解Gross profit is found as “sales revenue − cost of sales,” and here the cost of sales is “fixed cost + variable cost × number of units manufactured.” From Table 1 (in the lead text of q089), Plan A has a fixed cost of 14,000,000 yen per month and a variable cost of 60,000 yen per unit, so the cost of sales when manufacturing 400 units per month is 14,000,000 + 60,000 × 400 = 38,000,000 yen. To secure the target gross profit of 20,000,000 yen, sales revenue must be 38,000,000 + 20,000,000 = 58,000,000 yen, and since all units manufactured in the month are assumed to be sold within that month, the selling price is 58,000,000 yen ÷ 400 units = 145,000 yen. Written as a formula: selling price =(target gross profit + fixed cost)÷ number of units + variable cost per unit =(20,000,000 + 14,000,000)÷ 400 + 60,000 = 145,000 yen. This is exactly the lower limit that meets the target, so the answer to “what is the minimum price” is 145,000 yen (イ).
×Incorrectウ
At 150,000 yen the gross profit is 150,000 yen × 400 − 38,000,000 = 22,000,000 yen, so the target is achieved, but what is being asked is the minimum price. Since the cheaper price of 145,000 yen also secures 20,000,000 yen, this value is too high to be the lower limit.
×Incorrectエ
At 160,000 yen the gross profit is 160,000 yen × 400 − 38,000,000 = 26,000,000 yen, far exceeding the target, but this is not the minimum price either. The value that exactly meets the target, 145,000 yen, is the answer being sought.
ここがポイント
Gross profit = sales revenue − cost of sales; cost of sales = fixed cost + variable cost per unit × number of units manufactured (sold). Keep in mind that fixed costs stay constant regardless of the number of units, while variable costs are proportional to it.
The formula for working back from a target profit to the required selling price: selling price =(target gross profit + fixed cost)÷ number of units + variable cost per unit. When asked for the minimum, the answer is the value that exactly meets the target; a higher value still satisfies the condition but is not the lower limit.