Blending Problem

A blend is some combination of materials to make another material. Given raw materials, their blends make intermediate materials, called stock, and/or final materials, called products. The raw materials have purchase costs and the blending activities have costs of operation and maintenance. The products have either fixed demands or selling prices, and the problem is to find blends that minimise total net cost (or maximise profit).

Gasoline blending was one of the very first applications of linear programming to business problems. Example here is, of course, very much of an oversimplification of the real problem, but it captures the essential elements. But blending problems turn up in many contexts. Practical example of such a problem is the production of feeds for animals as well as some kind of human diets (for sportsmen, for ill people in hospitals ), similar are colour mixtures etc.

One example of such a problem is the production of feed for chicken, which should be made from several different kinds of grains. The manufacturer is constrained by the fact that the mixture must satisfy certain nutritional requirements (percentage of fat, total amount of vitamins per day etc.). But not all restrictions are so rigorous because the mixes must be acceptable for chicken.