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 b i 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.
KeywordsCash Flow Setup Time Linear Programming Problem Slack Variable Total Profit
Unable to display preview. Download preview PDF.
- 4.Cf. N. V. Reinfeld and W. R. Vogel (1958), pp. 122–125.Google Scholar
- 3.Cf. A. Henderson and R. Schlaifer, op. cit., p. 87.Google Scholar
- 4.Borrowed from A. Chames, W. W. Cooper, D. Farr, and Staff (1953).Google Scholar
- 3.Cf. A. Henderson and R. Schlaifer, op. cit., pp. 77f.Google Scholar
- 4.See, for example, A. Henderson and R. Schlaifer, op. cit., pp. 79ff., or R. L. Ackoff (1961), pp. 139–150.Google Scholar