The program shall not charge any fee to an enrolled eligible child or the child’s parents or legal guardians except that if prescription drug benefits are offered a co-pay not to exceed $3.00 may be charged. The program shall be funded by private donations and private and public grants. The health care corporation may provide free of charge administrative services to the program as approved by its board of directors and subject to the commissioner’s approval. A child shall be enrolled as follows:

  (a) Dependent on funding on a first-come, first-served basis unless a named child is part of a group of 10 or more children who are fully sponsored by private donations.

  (b) Without regard to health status.