We apply constrained optimization techniques to optimally allocate the bandwidth and power to the users in a cellular network. Partial frequency reuse with multiple users in the inner region and the outer region is considered as inter-cell interference mitigation scheme. We show that the maximization of the minimum rate under variable bandwidth and variable power can be transformed into a geometric programming problem and solved efficiently using disciplined convex programming. CVX is used to solve the transformed optimization problem. The optimal solution assigns all available bandwidth to the inner and the outer users and only the satisfactory level of power that the users achieve higher rates that the minimum required rate.