To maximize the limited spectrum among primary users and cognitive Internet of Things (IoT) users as we save the limited power and energy resources available, there is a need to optimize network resources. Whereas it is quite complex to study the impact of transmission rate, transmission power or transmission delay alone, the complexity is aggravated by the simultaneous consideration of all these three variables jointly in addition to a channel selection variable, since it creates a non-convex problem. Our objective is to jointly optimize the three major variables; transmission power, rate and delay under constraints of Bit Error Rate (BER), interference and other channel limitations. We analyze how total power, rate and delay vary with packet size, network size, BER and interference. The resulting problem is solved using a branch-and-cut polyhedral approach. For simulation of results, we use MATLAB together with the state-of-the-art BARON software. It is observed that an increase in packet size generally leads to an increase in total rate, total power and total transmission delay. It is also observed that increasing the number of secondary users on the channel generally leads to an increased power, delay and rate.