Abstract
Selecting diets by quantitative techniques is becoming increasingly common. Linear programming is the most popular technique for the selection of least cost mixes of food to meet specific nutritional requirements for a particular group of persons for either general health or disease-related reason. Hypertension is a silent killer and its prevalence rate especially in the developing countries, which has been mostly associated to demographic, environmental and genetic factors, is becoming alarming. The DASH diet has been clinically proven to prevent and control hypertension. In this paper, a model that provides a Daily Optimal (minimum cost) DASH Diet plan for people with hypertension is formulated. The objective is to obtain daily minimum cost diet plans that satisfy the DASH Diets’ nutrients Tolerable Upper and Lower Intake for different daily Calorie Levels. The formulated DASH diet model was further illustrated using real data set with food samples gotten from the DASH eating plan chart. A DASH diet model for a hypertensive person with a 2000-daily-caloric need was formulated and its optimal diet plan for a day obtained with a total cost of 944.41 Naira. Optimal diet plans for other recommended daily calorie levels were also obtained.
Highlights
The “diet problem” is a classical example of the application of linear programming method
We try to minimize the cost while guaranteeing certain and predetermined nutritional value. This linear programming diet problem has been applied for certain group of people for either general health or disease-related reasons
[7] Fletcher et al (1994) in their work discussed the use of mathematical modeling in presenting the relationship between acceptable diets and satisfactory nutrition. They deviated from the normal “diet problem” methodology where the objective function is to attain the minimum cost of the diet plan and used a different approach where the objective function is based on the food preferences of individuals
Summary
The “diet problem” is a classical example of the application of linear programming method. [7] Fletcher et al (1994) in their work discussed the use of mathematical modeling in presenting the relationship between acceptable diets and satisfactory nutrition They deviated from the normal “diet problem” methodology where the objective function is to attain the minimum cost of the diet plan and used a different approach where the objective function is based on the food preferences of individuals. In this paper we present the DASH diet plan as a reliable dietary approach for controlling the systolic high blood pressure problem especially to the hypertensive in developing countries. We formulate a DASH diet model that gives a minimum cost daily diet plan that meets the nutritional requirements for reducing high blood pressure for different recommended daily calorie levels using the linear programming approach. N is the number of food items; aij is the number of units of nutrients i one unit of food item j; bi is the specific number of units of nutrient i required; Cj is the cost of food item j; Xj is the number of units of food item j in the solution
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