Sample size of the strata is determined by the help of some allocation methods in Stratified Random Sampling. Most of the allocation methods ignore the selection cost. However, in real life applications it is very rare to come across such situations. In this study, a new compromise allocation method is proposed by adding a non-linear cost function constraint to Costa et al.(2004) method. Using this new allocation, the sample size with linear cost constraint is also obtained. The performance of the proposed method is studied utilizing the data from Statistics Canada's Monthly Retail Trade Survey (MRTS) of single establishments used by Choudhry et al. (2012).