7x + 4y > or equal to 400 which of the following constraints should be used to determine viable solutions

To determine the viable solutions for the inequality \( 7x + 4y \geq 400 \), we need to consider the context of the problem. Since viable solutions often pertain to scenarios such as optimization problems in linear programming, we typically look for solutions that fit the requirements specific to that context.

Given the options provided:

1. **A viable solution will have only positive whole numbers**: This option is common in many practical optimization problems where we might be dealing with quantities (like items, people, etc.) that cannot be negative or fractional.

2. **A viable solution can include fractional values**: This is possible in mathematical terms, but it depends on the context. If the context allows for fractions, then this is a valid consideration.

3. **There is only one viable solution**: This is unlikely for inequalities since they typically represent a region of solutions rather than a single solution.

4. **A viable solution can have positive and negative numbers**: This may not apply in many real-world scenarios, particularly those that require non-negative values (e.g., quantities cannot be negative).

### Conclusion:
The option that most likely fits typical constraints for problems involving variables like \( x \) and \( y \) in contexts such as financial figures, quantities of products, or similar entities would be:

**A viable solution will have only positive whole numbers**.

However, if the context allows for flexibility, check the specific requirements of your situation to determine if fractional values might also be allowed.