Linear programming, an operations research technique is widely used in finding solutions to complex managerial decision problems, but firms at Emene Industrial Layout make more use of the trial-and-error method. As such, firms at the Layout have been finding it difficult in allocating scarce resources in a manner that will ensure profit maximization or cost minimization. This study was carried out to seek and arrive at the optimal product-mix of a productive firm-the Golden Plastic Industry Limited- in the layout. The production problem of the firm was formulated as a linear programming problem and estimated as such. The result shows that only two sizes of the total eight “PVC” pipes should be produced. The study succeeded in establishing that Golden Plastic Industry Limited, Emene should produce 114,317.2 pieces of 25mm by 5.4m conduit pipes and 7,136.564 pieces of 20mm by 5.4m thick pressure pipes, and zero quantities of the rest sizes of pressure pipes per month in order to obtain a maximum profit of N1,964,537 given the present level of available funds and the technical coefficients of the products. The study also shows that only two of the raw materials –tio 2 and labour time- were surplus, while the other six-resin, calcium carbonate, stabilizer, cast, carbon black and blend-were scarce in relation to the formulated model. The shadow prices of the raw materials obtained showed their unit contribution to the objective function (profits) and suggests to management the prices at which they should either be bought or sold.