Whenever we think about questions such as the audience or purpose of a work of literature, often we need to infer the answer from the themes within the play. This play was not written for a specific audience, but rather it was for a general audience, consisting of both blacks and whites. The way that it presents the struggles of a black Chicago family and argues for racial tolerance seems to suggest that it was intended for a white audience just as much as a black audience.
Certainly, the presentation of the Younger family and the various trials they suffer due to their race indicates that race and racism are key elements of this excellent play. Race is shown to impact almost every single act they perform and their lack of opportunities and the struggles they face daily are a direct result of the colour of their skin. Their poverty is shown partly through the apartment where they live, which is not cared for properly by the owner. Travis is shown to chase a rat and Ruth fights battles to eradicate the cockroaches there--both features of life that many whites would never dream of experiencing in their own homes.
However, most important to this theme is the visit of Lindner and his attempt to dissuade the Youngers from moving to his neighbourhood. Being willing to pay off the Youngers for not moving into his neighbourhood, that he wants to be all-white, is a subtle and pervasive form of racism, made all the more dangerous because of its non-violent form.
In this play, therefore, Lorraine Hansberry seems to be presenting the realities of black life to her audience but also arguing for a more tolerant approach to race and racism. The intended audience, from what we can infer, was meant to be made up of both whites and blacks.