FileMaker can do what you describe. In fact, the starter solutions that come with FileMaker can do some of this though they would need modification to provide the complete system. (They can, however, serve as examples in how to manage, sales, purchasing and inventory.)
But the key question is "Can YOU do it with FileMaker?" This depends on both your skill and experience and on your ability to invest time in learning how to create the solution that you need or whether you can acquire the solution from a consultant or other third party source after they have used FileMaker to produce the solution.