In this paper, the problem of non-response with significant travel costs in multivariate stratified sample surveys has been formulated of as a Multi-Objective Geometric Programming Problem (MOGPP). The fuzzy programming approach has been described for solving the formulated MOGPP. The formulated MOGPP has been solved with the help of LINGO Software and the dual solution is obtained. The optimum allocations of sample sizes of respondents and non respondents are obtained with the help of dual solutions and primal-dual relationship theorem. A numerical example is given to illustrate the procedure.