Finding the largest possible voltage gain

Question

Solve the following problem:

Q: A BJT amplifier such as that in Fig. is to be designed to support relatively undistorted sine-wave output signals of peak amplitudes P volt without the BJT entering saturation or cutoff and to have the largest possible voltage gain, denoted Av V/V. Show that the minimum supply voltage VCC needed is given by

V_cc=V_cE_sat+P+|A_v|V_T

Also, find VCC, specified to the nearest 0.5 V, for the following situations:

(a) Av =-20 V/V, P = 0.2 V

(b) Av =-50 V/V, P = 0.5 V

(c) Av =-100 V/V, P = 0.5 V

(d) Av =-100 V/V, P = 1.0 V

(e) Av =-200 V/V, P = 1.0 V

(f) Av=-500 V/V, P = 1.0 V

(g) Av =-500 V/V, P = 2.0 V