Abstract: Described are methods and systems for estimating an optimal product pack size and on-shelf customer facing quantity of the products in view of shelf capacity limitations of the shelves at a given retail store/product distribution center, with the aim of maximizing the total net profit of the store/distribution center. The systems and methods obtain inventory-related, retail facility product storage capacity-related, and product storage/handling-related data from one or more databases and estimate the net profit of multiple variations of pack size and customer-facing quantity for each product. Then, these results are processed via various inventory optimization algorithms obtained from one or more databases to estimate the pack size and customer-facing quantity for each of the products to be stocked at the retail facility that would be estimated to result in maximum net profit for the retail facility within a given period of time.

Abstract: A method for converting methane by an oxidative coupling reaction to longer chain hydrocarbons comprising cofeeding methane and oxygen simultaneously and continuously into a reaction zone to form a mixture, contacting said methane and oxygen mixture under oxidative coupling reaction conditions with a solid catalyst consisting essentially of manganese oxide and silicon oxide, promoted with an alkaline metal and non metal, to form longer chain hydrocarbons wherein the manganese, silicon oxide, alkali metal and non metal are present in a molar ratio 0-0.5:93.2-93.7:4.2:2.1.

Abstract: An improved method for the oxidative conversion of methane into higher hydrocarbons in which methane and oxygen are continuously and simultaneously cofed into a reaction zone under effective oxidative coupling conditions and contacted with a solid catalyst consisting essentially of a catalyst having a composition of empirical formula Ce.sub.a Na.sub.b Ca.sub.100 O.sub.x wherein a is in the range 0.03 to 2.0, b is in the range of 0.7 to 7.0 and oxygen is present in a molar amount sufficient to fulfill the valence requirements of cerium, sodium and calcium.