One of the first practical problems to be formulated and solved by linear programming methods was the so-called diet problem, which is concerned with planning a diet from a given set of foods which will satisfy certain nutritive requirements while keeping the cost at a minimum. For each food the nutritional values in terms of vitamins, calories, etc. per unit of food are known constants and these are the a’s of the problem, a ij being the amount of the ith nutritional factor contained in a unit of the jth food. If it is required that there shall be at least bt units of the ith nutrient in the diet the nutritional requirements will take the form of a set of linear inequalities1 in the variables x j , which represent the amounts of the respective foods which shall be present in the diet. These restrictions will in general be satisfied by a large number of combinations of ingredients (foods) and we want to select a combination which minimizes the total cost of ingredients, i.e., a linear function in the x j where the coefficients c j are the prices per unit of the respective foods.
KeywordsSetup Time Linear Programming Problem Transportation Problem Slack Variable Total Profit
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