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Hanly and Yates proposed algorithms for combined power and cell (PIC) control that proved to be an optimal solution to P/C control if such a solution exists. Anpalagan and Sousa have proposed a combined rate, power, and cell (R/P/C) control algorithm with the main idea of interference balancing between base stations. They proposed an algorithm which was empirically proved to yield the optimal solution in terms of the average transmit bit energy of the system. In this paper, a mathematical proof is given that shows the optimality of the R/P/C algorithm. The R/P/C algorithm gives flexibility in setting the rate in response to the congestion level in the network, and hence, it has applications in the areas of delay-tolerant data services.