Diet problem by using Linear Programming


  • Shengtai Ding Author
  • Ruokai Wang Author
  • ke Hu Author



Optimization, minimize, standard form, canonical form, constraints


This paper will discuss the eating problems people encounter daily, mainly using Stigler’s idea. This dietary problem refers to how people can buy the food they need at the most affordable cost under balanced nutrition. Therefore, this paper uses linear programming to optimize this dietary problem. It contains nine nutrients, each of which has a minimum value. However, two of them, vitamin A and calcium, were set to have the highest intake amount. These intake settings are universal to all human beings, without exception. The algorithm applied to solve this linear programming is a simplex method, and a positive result is obtained. Our resulting minimum cost is even slightly cheaper than Stigler’s result. We conclude that if the taste of foods is not considered, people can obtain the required nutritional content by spending very little money. While it might not seem useful in modern countries, it is a meaningful investigation for underprivileged people who live in extreme poverty. However, the number of food considered in this paper is still limited. Also, the data we included come from the twentieth century for comparison with Stigler, which is already outof-date. Therefore, given that the diet problem is a topic worth investigating, further research with more comprehensive food choices and more up-to-date data is needed.