Constant MC - Monopolstic Competition I would like to know if it is possible to have constant marginal costs (MC) in a business that is operating on a market, that is defined by monopolistic competition?

The company is a construction company, more specific a scaffolding company. My assumption is based on:


They have invested in their building materials one time. This means that they have a natural limit on how much work they can do. 
They don't expect to buy more building materials in order to do more work, since they are also limited by number of employees.
All employees are on a fixed salary.
The only variable cost that is associated with each construction job is the transporation to/from site.


Since there is only one variable cost - the transportation, I am assuming that the marginal costs are constant, since transportation doesn't cost more whether they have 1 site (Q) or 10 sites (Q) to maintain.

Is this a valid assumption? Is it possible to have a constant MC such a market?
It is possible for firms to have constant marginal costs in monopolistic competition in theory. Nevertheless, they must also have fixed costs. The fixed costs prevent firms from entering in sufficient numbers such that you would have perfect competition. 

As to whether constant marginal costs are realistic in you scenario, that depends on what you believe about the industry in practice. That would require detailed knowledge and expertise of this specific industry, which you are unlikely to find on this site.

Note, however, that just because the company has already bought the materials does not neessarily mean that these costs do not matter. For example, the company may still want to use less material per production output, because it could resell the unused materials. So the company in that case still cares about the costs associated with the use of each unit of material.

It is a bit unclear in your example what this company actually produces. However, if you think the costs of producing one extra unit are the same, regardless of how many units you have already produced, then you are justified in assuming constant marginal costs.