First of all, usually support functions are classified as fixed costs. To understand why, we need to take a look at:
- Definition of fixed and variable costs
- Type of expenses behind what you call support functions
Fixed costs are the costs that aren't dependent on the level of goods/services produced. Variable costs change in proportion to level and services produced.
Support function costs are expenses associated with HR, Accounting and other corporate staff, which aren't influenced by the amount of goods/services produced. Therefore, support functions are fixed costs.
However, we could argue that if production of goods increases by a big enough amount (company grows), we will need to hire additional corporate staff, but in this case the costs will be classified as stepped fixed costs.
In any case, it looks like you are trying to understand how you could break down costs in a structured way. I would like to point out that fixed/variable split isn't the only one avaiable. There are different ways how you could break down costs (e.g. direct/indirect), and although fixed/variable is the most common one, it doesn't mean that it will be the correct one in a case that you receive. It's better to ask interviewer first about the preferred way of cost break-down.
Moreover, labor isn't always fixed cost. Actually, in managerial accounting labor is classified most often as a variable cost. The are many reasons for that, but for simplicity sake, you could use a simple rule of thumb:
- if employees are paid by hour - variable costs
- if employees get monthly salaries - fixed costs
Hopefully it helps.