To justify spending on any project, you have to explain why it is worth spending money on. This is standard practice for any large expenditure.
It's a simple concept, but it's hard to do well.
Simply identify the benefits of hiring someone, and their value. If the additional value is more than their cost, by the required return, they'll spend the money.
If you spend your time doing other stuff, point out you spend x% of your time doing this other stuff, and if you consider the context switching overhead you're very inefficient. That's often enough to hire a jr support guy.