In the present day high-tech uncertain industrial environment, there is often a need for determining expected cost per piece or per batch in advance of production. A mathematical model for stochastic cost optimization has been developed. If an exact solution is desired, a two stage stochastic geometric program has to be solved. This is tedious and requires great computational effort. However, managers are often concerned with a policy decision which can be based on the probable lower and upper bound on the stochastic cost function. This paper deals with estimating the probable cost range and also calculating the exact expected cost. The probability level on the lower bound of cost has been calculated through the theory of error propagation. A decomposition algorithm has been used to find the exact expected cost under a set of real-world constraints. The whole approach has been explained through an example