ABSTRACT

 In these problems, we determine the number of units of different products which should be produced and sold by a firm when each product requires a fixed manpower, machine hours, labour hours per unit of product, warehouse space per unit of the output etc., in order to make maximum profit.Mathematical Techniques such as George Dantzig Simplex Method are used in Computer modelling (simulation) to find the best possible solution in allocating limited resources — energy (electrical or mechanical), machines (electrical/mechanical), materials/units (the case of study for this research), money, personnel, space, time, etc. to achieve maximum profit or minimum cost. However, it is applicable only where all relationships are linear and can accommodate only a limited class of cost functions — linear programming. This research work investigates the possibility of maximizing the profit of a mechanical product manufacturing business by optimizing the production units using linear programming tool under varying constraints. Numerical analysis used was the Simplex Method for simplifying the developed industrial linear programming problem. The foundry Company, CHAMPION BLACKSMITH LTD., Rivers State, Nigeria was used as a case study. The foundry Companyis known for its four major units produced which include aluminium spoon, 5 litre bowl, grinding teeth plate of aluminium and 5 litre pot, all by casting. Time for varying operations such as moulding, casting (pouring and solidifying) and finishing were collected for each product at the Industry. A mathematical model equation for profit was developed based on the previous profit data of the foundry and subjected to constraint equations based on the time required to finish each of the three products denoted p, q, r and s. The profit function was analysed arithmetically (using the Simplex Method) and by MATLAB program (developed based on the Simplex Method/Algorithm) in order to obtain the quantity of each product that will give maximum profit. The result obtained revealed that approximately