Maximizing Production of Product A

A company manufactures two products, $A$ and $B$. The production cost, $C$, for producing $x$ units of product $A$ and $y$ units of product $B$ is defined by the linear equation:

$$C = 20x + 15y$$

The company has a budget of $600 for production costs. Additionally, they can produce a maximum of 30 units of product $A$ and 25 units of product $B$. Find the maximum number of units of product $A$, $x$, that the company can produce while maximizing the total production.