In the "Sydney Morning Herald" of 23 March 2005, Ross Gittins argued that the funding arrangements for private schools positively encourage parents to move their children from the state system. The then Federal Minister for Education, Dr Brendan Nelson, in a letter to the "Herald" of 25-27 March, responded by saying that 68% of all school pupils go to state schools, and those students receive 76% of Government funds allocated to the totality of all pupils attending schools. He stated also that the policy of subsidising pupils who went to a private school resulted in taxpayer savings of $4 billion. However, the Minister's response did not address the extent to which more money could possibly be saved by having a different subsidy from the one currently offered by the Government. There are two conflicting factors in offering subsides to private school pupils. On the one hand, the greater the subsidy per pupil, the more pupils will enrol in private schools. On the other hand, the greater the subsidy per pupil the less money will be saved each time a pupil enrols in a private school. How do these factors balance out, and where would an optimal subsidy occur? The problem is closely related to other problems of optimisation that arise in business, industry and public policy. In this article, the author discusses how this problem can be modelled mathematically by means of a quadratic function that describes how the savings change as the subsidy changes. (Contains 3 figures.)