In the United States, public universities may choose to license a plant variety to a limited number of producers (an exclusive license) or to an unlimited number of producers (an open license). This choice has implications for the quantity and distribution of total benefits from the variety. Universities have traditionally released new apple varieties under open licenses, but several universities have now begun exploring or implementing exclusive licensing. In this paper, we consider the choice faced by a public university when licensing a plant variety patent, with a focus on apples. Our work differs from the majority of past studies on patent licensing because we allow licensees to determine the signal of product quality through a trademark and we consider welfare objectives for a public university that differ from simple maximization of patent income. In this context, we compare monopoly licensing and two oligopoly licensing scenarios. We then solve for the optimal choice of licensing fees for the university. Using numerical simulations, we find that consumer surplus and social welfare may be higher under exclusive licensing if consumers are relatively responsive to expenditure on the trademark but relatively insensitive to price. However, exclusive licenses may create distributional concerns among producers. Furthermore, different objective functions of the university can imply different optimal outcomes for both the number of licensees and the licensing fees. Although we focus on apples, this model and its results could apply in a variety of settings.