Is it permissible to work as a programmer for a company that sells alcohol, at its administrative headquarters, if the work involves programs and applications that help manage its sales and purchases?

If your work in the company is not connected to haram (forbidden acts) or assisting in it, then there is no harm in working there. The fact that some of the company's products are forbidden does not affect this. However, if you know that the programs you are working on are used to promote or sell alcohol, then it is not permissible for you to work with them in this case.