> Yes, you have quantity, but what about quality? How much time will you spend sorting the wheat from the chaff? How much application spam will you have to review and dispose of? And of the relevant ones, how many under- and over-qualified candidates do you need to sift through because they lacked the vital piece of information that is a salary range?
It's easy: filter the incoming candidates based on who you want to hire. Send your favorite candidates a simple email saying what you want to pay for that position, and ask if they're still interested. Interview the ones that are. (This way, you're not posting the salary number to the public, but you're still filtering candidates quickly and respecting their time.)
If none of your favorite candidates are interested at your targeted price, there's your answer. Either lower your standards and take one of the other applicants, or ask all of your favorite candidates what number it would take to get them interested. (No interviewing - you don't have the right to take up their time until you can come up with the money - you're just asking for the salary number they would need to even step into an interview.) When the numbers come back, that's what it would take to hire your favorite candidates.