A problem often of concern to managers in processing industries is blending. Consider the task facing Lisa Rankin, procurement manager of a company that manufactures special additives. She must determine the proper amount of each raw material to purchase for the production of a certain product. Each gallon of the finished product must have a combustion point of at Least 2200E. In addition, the products gamma content (which causes hydrocarbon pollution) cannot exceed 6 percent of volume, and the product’s zeta content (which cleans the internal moving parts of engines) must be at least 12 percent by volume, three raw materials are available. Each raw material has a different rating on these characteristics.

Raw material A costs $0.60 per gallon; raw materials B and C cost $0.40 and $0.50 per gallon respectively. The procurement manager wants to minimize the cost of raw materials per gallon of product. Use linear programming to find the optimal proportion of each raw material for a gallon of finished product.

Raw Material A B Characteristic Combustion pointF Gamma contest (%) Zeta content (%) 200 180 20 4310 20 10