Historically, the field of linear programming was developed by George B. Dantzig and his associates during World War II and was first used by the U.S. Air Force as an aid in decision making. Today it application to a wide variety of problems. Some of these are as follows:

(i)    Diet Problems. To determine the minimum requirement of subject to availability of foods and their prices.

(ii)    Manufacturing Problems. To find the number of items of each type that should be manufactured so as to maximize the profit subject to production restrictions imposed by limitations on the use of machinery and labour.

(iii)    Transportation Problems. To find the least costly way of transporting shipments form the warehouses to customers.

(iv)    Blending Problems. To determine the optimum amount of several constituents to use in producing a set of products while determining the optimum quantity of each product to produce.

(v)    Assembling Problems. To have the best combination of basic components to produce goods according to certain specifications.

(vi)    Production Problems. To decide the production schedule to satisfy demand and minimize cost in face of fluctuating rales and storage expenses.

(vii)    Job Assigning Problems. To assign job to workers for maximum effectiveness and optimum results subject to restrictiosns of wages and other costs.

(viii)    Trim-Loss Problems. To determine the best way to obtain variety of smaller rolls of paper form a standard width of roll that is kept in stock and, at the same time, minimize wastage.

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