Example 3 If a store sells a certain product, which costs 100 yuan, at 120 yuan, it can sell 300 units. If the price of the product is increased by 1 yuan based on 120 yuan, it will sell 10 fewer units, and if the price is reduced by 1 yuan, it will sell 30 more units. Question: To maximize profit, what price should the store set for the product?
Solution: (1) If sold at 120 yuan each, 300 can be sold, and the profit is $300 \times 20 = 6000$ (yuan).
(2) If the price is increased by $x (x > 0)$ yuan, then (300 $- 10x$) can be sold. Let the profit be $y$ yuan, then
$$
\begin{array}{l}
y = (20 + x)(300 - 10x) \\
= -10x^2 + 100x + 6000 \\
= -10(x - 5)^2 + 6250 .
\end{array}
$$

Because $-100)$ yuan, then (300 $+ 30x$) can be sold. Let the profit be $y$ yuan, then
$$
\begin{array}{l}
y = (20 - x)(300 + 30x) \\
= -30x^2 + 300x + 6000 \\
= -30(x - 5)^2 + 6750 .
\end{array}
$$

Because $-30 < 0$. So,
When $x = 5$, $y_{\text{max}} = 6750$.
Therefore, when the price is reduced to 115 yuan, the maximum profit of 6750 yuan can be obtained.

In conclusion, when the price is set at 115 yuan, the store can achieve the maximum profit.