A LINEAR PROGRAMMING MODEL FOR A DIET PROBLEM

Abstract

In this paper we solve a diet problem which has the goal to find an optimal combination of proposed foods on the condition that the daily nutritional requirements of a person are satisfied. First of all, we find the nutrient content of our proposed menu which a person generally consumes, throughout an entire day, 1 or 2 portions of some given foods (yogurt, cereals, rye bread , Feta cheese, coffee, chicken soup, baked salmon, boiled potatoes, lemon juice,  dry wine, ice with milk and vanilla, spaghetti in tomato sauce with cheese, apple juice). Secondly, we search for quantities of all specified items of the same menu as the diet amount of calories is 2200 Kcal / a day, respectively 2500 Kcal / a day. Finally, we search for quantities of the same proposed menu, using linear programming techniques, as the diet contains minimum amount of calories. The mathematical model of the problem is formulated as a linear program where the objective function is the total amount of calories for the proposed menu, on the condition that the constraints regarding the amounts of protein, vitamins, minerals, fats, dietary fiber consumed throughout an entire day are satisfied. We solve this problem by using the Sover tool in MS Excel and we describe all the steps involved in solving the linear programming model in the context of the menu proposed by us.