In the survey, it is very hard to get the complete response. Because the respondents tend to refuse to the questionnaire with something like incomes of the individual or may not be at home in the survey time. These nonresponses are classified into two groups as the item nonresponse and the unit nonresponse. When the nonresponse happen to the special item of the questionnaire, it is caned item nonresponse. On the other hand the unit nonresponse occurs to the totally missing in questionnaire. In this paper, we only consider to the unit nonresponse situation. We propose that the optimal estimator which is minimized the variance of the estimator under a fixed cost function for the survey and response.