Image classification is a fundamental building block for a majority of computer vision applications. With the growing popularity and capacity of machine learning models, people can easily access trained image classifiers as a service online or offline. However, model use comes with a cost and classifiers of higher capacity usually incur higher inference costs. To harness the respective strengths of different classifiers, we propose a principled approach, OCCAM, to compute the best classifier assignment strategy over image classification queries (termed as the optimal model portfolio) so that the aggregated accuracy is maximized, under user-specified cost budgets. Our approach uses an unbiased and low-variance accuracy estimator and effectively computes the optimal solution by solving an integer linear programming problem. On a variety of real-world datasets, OCCAM achieves 40% cost reduction with little to no accuracy drop.