Network Flow in Graph Theory - The Producer's Problem

The Producer's Problem refers to a manufacturer in the economy, aiming at picking a production strategy that will maximize his gain, confronting the constraints of production. The book gives a general solution to The Producer's Problem based on various constraints applicable to the system. Every producer or manufacturer in the economy possesses a limited amount of resources required for production ie, raw materials, service and capital. The producer has to work his way through the raw materials at hand, service available and his investment to maximise his profit by minimising the cost involved. At every stage of manufacturing, there are several production units or factories that carry out the same process but which has different cost of production and freight charges per unit. The producer in this problem desires to select a rational strategy in order to minimise his total cost of producing a fixed number of items in a given set-up and the book describes the solution using linear programming. The problem is then generalised so that it may be applied to any similar situation.