What risks do we run if older worker loses job in restructuring?

Q. We’re a small business (just eight employees) and haven’t laid anyone off. But business is slow and we need to restructure. We have an employee who has worked here part time (12 hours per week) for 25 years. She is 65 years old. We have one other part-timer (10 hours per week) who has worked here just one year. We’d like to lay off both part-time employees and keep the full-time employees. Can we do that?