The present study addresses the problem of minimum cost and precision in the estimation of the population mean in the presence of nonresponse and measurement errors. It is assumed that both the survey variable and the auxiliary variable suffer from nonresponse and measurement errors in the second phase sample. A ratio, exponential ratio-ratio type, and exponential product-ratio type estimators of the population mean are proposed using the information on a single auxiliary variable. The expression of biases and mean square errors of the proposed estimators are obtained up to the first order of approximation. The cost of the survey is studied theoretically. The optimum stratum sample size and the inverse sampling rate are derived. It is noted that the size of the sample to be selected increases with the increase in the cost of the survey. A minimum mean square error is attained when the cost of the survey is high.