## Abstract

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 *i*th nutritional factor contained in a unit of the *j*th food. If it is required that there shall be at least *b*_{ i } units of the *i*th nutrient in the diet the nutritional requirements will take the form of a set of linear inequalities^{1} 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.

## Keywords

Cash Flow Setup Time Linear Programming Problem Slack Variable Total Profit## Preview

Unable to display preview. Download preview PDF.

## References

- 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