Suppose in the waterfilling algorithm that instead of log(1 + a_i P_i) the utility function was tan^-1(a_i P_i). i.e. the waterfulling optimisation problem became max sigma_i tan^-1 (a_i P_i) Subject to P_i greaterthanorequalto 0 i = 1, ..., N P_1 + ....+ P_N = P i. Determine the equivalent of equation (1) on slide 13 of the notes on waterfilling. ii. What interpretation can be given to the nature of the utility function used? Explain. Suppose in the waterfilling algorithm that instead of log(1 + a_i P_i) the utility function was tan^-1(a_i P_i). i.e. the waterfulling optimisation problem became max sigma_i tan^-1 (a_i P_i) Subject to P_i greaterthanorequalto 0 i = 1, ..., N P_1 + ....+ P_N = P i. Determine the equivalent of equation (1) on slide 13 of the notes on waterfilling. ii. What interpretation can be given to the nature of the utility function used? Explain