Name: shams
Who is asking: Student
Level: Secondary

Question:
What is Linear programming and optimization

Hi Shams

Linear programming and optimization is part of a branch of mathematics called operations research. Operations research is concerned with optimal decision making in, and modelling of, systems that originate in real life. The use of the word optimal here is important as one of the major themes in operations research is this "search for optimality". Rather than being content with merely improving the status quo, the goal is to identify the best possible course of action.
    Operations research began in the military during World War II in an attempt to optimally allocate scarce resources to the various military operations. Linear programming, developed in 1947, is one of the techniques that is used formulate and study certain kinds of optimality problems. It is now widely used in many areas including the petroleum industry, the food processing industry, iron and steel, paper mills, automobile manufacturing, financial institutions, hospitals, government agencies, almost anywhere you can imagine. A specific example is the recipe for sausage. Each commercial sausage maker has their own recipe for the different ingredients. But any commercial cook will tell you that ingredients for recipes can be plus or minus 10%, so the "cooks" know that they have an upper and lower limit for each of the ingredients. The specific recipe for each day is developed to optimize, in this case minimize, the cost, depending on the costs of the various ingredients that day. Here, as is the case for all linear programming problems, the mathematical description is in terms of linear equations and linear inequalities.

Cheers
Jack and Penny