This paper describes a multi-objective goal programming (MOGP) model that has been developed for a machine tool manufacturing industry to find the optimum production plan as a means to know what products to be considered and how much to be produced. Performance criteria such as gross profit, product quality, machine utilisation, production cost and work-in-process (WIP) inventory were identified as multi-objectives. Lexicographic goal programming modelling approach was applied to solve the proposed multi-objective model. In order to demonstrate the capability of the developed linear MOGP model, a pre-emptive goal priority structure has been formulated in consultation with the company. The sensitivity of the MOGP model was tested with respect to alterations in the order of goal priorities and changes in parameter values. The insights gained from the sensitivity analysis will assist the similar companies to find out an optimal level of production activities on par with the organisational goals.