If a book published by a publishing house is published at a price of 15 yuan per book, 40000 copies can be published.

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.

Answer 1

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.