To find two numbers with a maximum product and a sum of 7, we can use the following steps:
1. Let's denote the two numbers as x and y.
2. Since we want to maximize the product of the two numbers, we need to make them as close as possible. This means they should be close to each other without being equal.
3. Considering the sum of the two numbers is 7, we can set up an equation: x + y = 7.
4. To maximize the product, we can choose two numbers that are closest to each other, which are 3 and 4.
5. Therefore, the two numbers with a maximum possible product and a sum of 7 are 3 and 4.
6. The product of 3 and 4 is 12, which is the maximum possible product for two numbers with a sum of 7.
