Flour factory was producing two distinct types of products two types of flour and wheat meal. Hence, to collect data two sources of data are used. Those are primary and secondary data. Especially to get information on the production and profit analysis of the factory understudy, an interview was conducted with the manufacturing manager, co-managers, persons working on Machine, laboratory and electricity technician, labor workers and the sales managers of the factory and data collected on the unit costs of production of the products, the unit selling price of the products and also contacted the sales and the purchasing, production and marketing managers of the factory. The secondary data sources were obtained from document analysis of the factory production from its establishments up to now. Therefore, the study aims to analyze the total production and profit of this factory by solving a mathematical modeled to a linear programming problem. Hence, the targeted research population is 37 persons are selected; those have direct influence (factors) on the production of this factory. Hence, a collected data were transformed into a linear programming model and the modeled data was solved by the method of simplex algorithm or by using MS-Excel solver to analyze total production and profit of the factory within the available scarce resources. Linear programming optimizes (maximizing or minimizing) a dependent variable subject to a set of independent variables in a linear relationship, given a number of linear constraints of independent variables. The value of dependent variables which is the value obtained from solving the problem is subject to the independent variables set by the decisionmaker (or determined by solving the problem). The independent variables in linear programming are known as variables of unknown value, and the decision-maker has to calculate the value of such variables by solving the problem. Thus, a general form of a linear programming problems for ' n ' decision variables and ' n ' constants can be written as follows; MaximizeP=a1x1+a2x2++anxnSubjecttob11x1+b21x2++bn1xnd1b12x1+b22x2++bn2xnd2b1mx1+b2mx2++bmnxndmWith,x1,x2,x3,,xn0