If a book published by a publishing house is published at a price of 15 yuan per book, 40000 copies can be published.
2024-09-16 07:03
If a book published by a publishing house is published at a price of 15 yuan per book, 40000 copies can be published. When the price of each book increases by 1 yuan, the circulation will decrease by 2000 copies.
1 answer
每本书籍的定价提高1元可以发行的书的数量就会减少本。 假设最初有$x$本书每本定价为$y$元那么根据题意可以列出以下方程组: $$ \begin{cases} x = 40000 \\ y \cdot (1 + r) = 40000 \cdot (1 + r) + x \end{cases} $$ 其中$r$ 表示每本书的利润率。 将第一个方程式代入第二个方程式中得到: $$ \begin{aligned} y \cdot (1 + r) \cdot (1 + r) &= 40000 \cdot (1 + r) + x \\ y^2 + ry + r^2 &= 40000 + x \\ r &= \frac{1}{2} - \frac{1}{y^2} \\ \end{aligned} $$ 解出 $r$ 的值即可得到每本书的定价 $y$ 的值。 当每本书的定价每提高1元时可以发行的书的数量为: $$ \begin{aligned} x' &= \frac{x - (40000 \cdot (1 + r) + x)}{1 + r} \\ &= \frac{x - 40000 \cdot (1 + r) + x}{1 + r} \\ &= \frac{x}{1 + r} \\ \end{aligned} $$ 因此每本书的定价提高1元时可以发行的书的数量为原来的 $\frac{1}{1 + r}$ 倍。
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