To solve part (a) of the problem, we need to determine the maximum value of $a + b$ given the constraints:

• $a$ can be either 4 or 5.
• $b$ can be either 1 or 2.

Let's evaluate all possible combinations of $a$ and $b$ to find the maximum value of $a + b$:

1. If $a = 4$ and $b = 1$, then $a + b = 4 + 1 = 5$.
2. If $a = 4$ and $b = 2$, then $a + b = 4 + 2 = 6$.
3. If $a = 5$ and $b = 1$, then $a + b = 5 + 1 = 6$.
4. If $a = 5$ and $b = 2$, then $a + b = 5 + 2 = 7$.

The maximum value of $a + b$ is:

$\boxed{7}$

Would you like to go through the other parts (b) to (h) as well, or do you have any questions about this part?

Here are some related questions:

1. How would you find the minimum value of $a + b$?
2. What are the steps to determine the maximum value of $ab$?
3. How can you calculate the minimum value of $a - b$?
4. What method would you use to determine the maximum value of $\frac{a}{b}$?
5. How do you find the maximum value of $a^2 - b^2$?

Tip: Always list all possible combinations when dealing with maximum or minimum problems to ensure you cover all scenarios!