With the edge computing becoming an increasingly adopted concept in system architectures, it is expected its utilization will be additionally heightened when combined with deep learning (DL) techniques. The idea behind integrating demanding processing algorithms in Internet of Things (IoT) and edge devices, such as Deep Neural Network (DNN), has in large measure benefited from the development of edge computing hardware, as well as from adapting the algorithms for use in resource constrained IoT devices. Surprisingly, there are no models yet to optimally place and use machine learning in edge computing. In this paper, we propose the first model of optimal placement of Deep Neural Network (DNN) Placement and Inference in edge computing. We present a mathematical formulation to the DNN Model Variant Selection and Placement (MVSP) problem considering the inference latency of different model-variants, communication latency between nodes, and utilization cost of edge computing nodes. We evaluate our model numerically, and show that for low load increasing model colocation decreases the average latency by 33% of millisecondscale per request, and for high load, by 21%.