A study on the optimization problems to find forebode shapes with minimum wavemaking and frictional resistance was performed. The afterbody was fixed as a given hull and only forebode offsets were treated as design variables. Design variables were divided into the offsets of given hull and small variation from them. For the wavemaking resistance calculation, Neumann-Kelvin theory was applied to the given hull and thin ship theory was applied to the small variation. ITTC 1957 model-ship correlation line was used for the calculation of frictional resistance. Hull surface was represented mathmatically using shape function. As object function, such as wavemaking and frictional rersistance, was quadratic form of offsets and constraints linear, quadratic programing problem could be constructed. The complementary pivot method was used to find the soulution of the quadratic programing problem. Calculations were perfomed for the Series 60 $C_{B}$=0.6. at Fn=0.289. A realistic hull form could be obtained by using proper constraints. From the results of calculation for the Series 60 $C_{B}$=0.6, it was concluded that present method gave optimal shape of bulbous bow showing a slight improvement in the wave resistance performance at design speed Fn=0.289 compared with the results from the ship theory only.