Stratified random sampling is an effective sampling technique for estimating the population characteristics. The determination of strata boundaries and the allocation of sample size to the strata is one of the most critical factors in maximizing the precision of the estimates. Most surveys are conducted in an environment of severe budget constraints and a specific time is required to finish the survey. So cost and time are especially very important objectives of most surveys thus they are necessitating to be under consideration. The study suggested Mathematical goal programming model for determining optimum stratum boundaries for an exponential study variable under multiple objectives model when cost and time are under consideration. To evaluate the performance for the suggested model for the exponential distribution a numerical example is presented. The results of the suggested mathematical goal programming are satisfying.