We explore the duality between lossy compression and channel coding in the operational sense: whether a capacityachieving encoder-decoder sequence achieves the rate distortion function of the dual problem when the channel decoder [encoder) is the source compressor [decompressor, resp). We show that, if used as a lossy compressor, the maximum-likelihood channel decoder of a randomly chosen capacity-achieving codebook achieves the rate-distortion function almost surely. However, operational duality does not hold for every capacity achieving encoderdecoder sequence. We show that there exist optimal channel coding schemes, which operate far from the rate-distortion function when used for the dual lossy compression problem. Index Terms: Channel coding with cost constraints, discrete memoryless sources, lossy data compression, rate-distortion theory,source-channel coding duality.