Science Journal of Applied Mathematics and Statistics 2020; 8(5): 59-66 http://www.sciencepublishinggroup.com/j/sjams doi: 10.11648/j.sjams.20200805.12 ISSN: 2376-9491 (Print); ISSN: 2376-9513 (Online) Analysis of Diet Choice towards a Proper Nutrition Plan by Linear Programming Tanzila Yeasmin Nilu 1, * , Shek Ahmed 2 , Hashnayne Ahmed 2 1 Department of Computer Science and Engineering, Green University of Bangladesh, Dhaka, Bangladesh 2 Department of Mathematics, University of Barishal, Barishal, Bangladesh Email address: * Corresponding author To cite this article: Tanzila Yeasmin Nilu, Shek Ahmed, Hashnayne Ahmed. Analysis of Diet Choice towards a Proper Nutrition Plan by Linear Programming. Science Journal of Applied Mathematics and Statistics. Vol. 8, No. 5, 2020, pp. 59-66. doi: 10.11648/j.sjams.20200805.12 Received: August 9, 2020; Accepted: August 25, 2020; Published: September 21, 2020 Abstract: Linear Programming is an optimization technique to attain the most effective outcome or optimize the objective function (like maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships called the constraints. In this paper, we have discussed fundamental and detailed techniques of formulating LPs models in various real-life decision problems, decisions, works, etc. In the human body, an unhealthy diet can cause a lot of nutrition-related diseases. Sometimes, having a proper diet costs beyond one’s limit and it affects us to develop a diet based budget-friendly nutrition model. Our goal is to minimize the total cost considering the required amount of nutrition values required. To construct the study we took some standard values of nutrition ingredients to compute the budget-friendly values. It's quite hard to resolve most of the real-life models with a large number of decision variables & constraints by hand calculations implies the use of AMPL (A Mathematical Programming Language) coding to get the optimal result. The number of variables & constraints isn't mattered in any respect for the computer techniques used in this study. This study results in some standard values of diet plan for optimizing the nutrition for a particular person with limited costs. Keywords: Optimization, Linear Programming Diet, Optimization Model, Real-Life Application, AMPL, Computer-Based Program 1. Introduction In practical life, we have to decide every step. While decision making we seek to answer the question `what is best?’ Always we want the best output with limited resources. A typical example would be taking the limitations of materials and labor and then determining the “best” production levels for maximal profits under those conditions. A linear programming (LP) problem is an optimization model by which we can optimize a measure of effectiveness under conditions of allocating scarce resources and before doing that we have to formulate LP according to the given restrictions. The problem of solving a system of linear inequalities dates back at least as far as Fourier, after whom the tactic of Fourier-Motzkin elimination is named. Linear Programming (LP) was first developed by Leonid Kantorovich in 1939 [2]. It had been used during World War II to plan expenditures and returns to cut back costs to the military and increase losses to the enemy. The three founding figures within the subject are considered to be Leonid Kantorovich, who developed the earliest LP problems in 1939, George Dantzig, who published the simplex method in 1947, and John mathematician who developed the speculation of the duality in the same year [1, 3]. The method was kept secret until 1947 when George B. Dantzig published the simplex method and John mathematician developed the idea of duality as a linear optimization solution and applied it in the field of game theory. Postwar, many industries found their use in their daily planning. The LP problem was first shown to be solvable in polynomial time by Leonid Khachiyan in 1979, but a much bigger theoretical and practical breakthrough within the field came in 1984 when Narendra Carmaker introduced a replacement idea named, the interior-point method for solving LP problems.