Investigation of the prospects of a joint venture-ship between two Firms in Ghana is reported. The novelty of this work is in the fact that it explores the ground of co-operation instead of competition that characterise the operations of these Firms. The goal was to find an optimum investment which was more profitable to both in a joint investment than in separate ones using linear programming (LP). LP models for both Firms were first formulated separately (one of them in an earlier work) using data and information obtained from both, following which a joint problem was posed, formulated, and solved. A sensitivity analysis was performed on the solutions to assess the stability of the models and the results used to determine range of possibilities for the optimum solutions for the Firms separately and jointly. The results showed that a joint investment could prove more rewarding for the two Firms than in separate investments.