ABSTRACT:
Operations research or mathematical optimization is the selection of a best element (with regard to some criteria) from some sets of available alternatives. An optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed sets and computing the value of the function. Linear programming (LP) is a technique for determining the optimum schedule of the interdependent activities in view of the available resources as it applies to the optimization models in which objectives and constraint functions are strictly linear. It is therefore imperative to apply optimization model in the cost of production and resource management in order to manage the use of raw materials and resources for effective optimal production which will result into maximum profit or low cost of production. It may be observed that optimization concept is rarely applied in the small and medium enterprise; in this era where many government policies encourage entrepreneurship. This study thus embarks on the method of finding and arriving at the optimal product-mix of an indigenous manufacturing company (ESC-Souvenir) that is engaged in leather production. The challenge encountered in getting the right proportion of raw materials needed during production was modelled as linear programming problem. The result shows that for the firm to obtain an optimal percentage production and an average monthly profit of 20%, thirty-nine thousand, six-hundred naira (N39,600 i.e. USD 396) will be needed for the production and supply of Types A, B and C custom-designed bags. The firm must vary the input values as a combination of thirty (30) of Type B and ninety (90) of Type C for the three products under consideration. The result also revealed that (for an optimal production level) the raw materials, leather/lining, parking foam and leather tape must be 54.4%, 25% and 32.5% in appropriate proportion respectively.
Keywords: Linear programming, Mathematical optimization, Operations research
