To solve part (a), we need to express $y$ in terms of $x$ from the equation:

$x + y = 230$

Step for (a):

1. Subtract $x$ from both sides to isolate $y$: $y = 230 - x$

Thus, the answer for part (a) is:

$y = 230 - x$

Would you like further assistance with the next steps or a deeper explanation?

Here are 5 related questions that could expand your understanding of optimization:

1. What method can we use to maximize the product $P = xy$ in this scenario?
2. How do we apply derivatives to find the maximum value of a function?
3. What conditions need to be met to ensure $x$ and $y$ remain nonnegative?
4. How does rewriting one variable in terms of another help in solving optimization problems?
5. What are some other applications of maximizing a product given a sum constraint?

Tip: In optimization problems, always rewrite one variable in terms of the other when possible. This simplifies calculations and helps find optimal solutions effectively.