Portfolio optimization is a major concern of individuals and businesses across the world for sustainable financial and economic management of their funds. This work, as a first part of a portfolio optimization study of two selected businesses in Ghana, is aimed at optimizing separately the investments of the two businesses, to maximize their returns and minimize their risks under their operational constraints. The problems, being multi-objective in character, were modeled with the expected returns on their investments and the variances/standard deviations of the returns over fixed periods of time as the objective functions. To ensure dimensional uniformity, the objective functions were normalized and the Weighted Sum scalarization method employed in MATLAB to find Pareto optimal solutions of the models, using data from the two businesses. The results reveal that weight variations do not necessarily lead to many varied or diversified Pareto optimal solutions. The three distinct Pareto optimal solutions obtained for one of the businesses, however, suggest that the business could make respectively about 104.45M, 15.70M, and 15.72M Ghana Cedis returns on its investments with risk to return margins of 0.225%, 1.77%, and 1.76% respectively. The other business with only two distinct Pareto optimal solutions could make 14.67M or 30.36M Ghana Cedis returns with corresponding risk to return margins of 0.016% and 0.017% respectively. It is recommended therefore that the businesses could select the solution with the least risk to return margins for implementation. A second part of the work, which will be reported in another paper, would investigate the models under post-optimality analysis and the prospects for a joint investment by the two businesses.