The final thesis written for the Quantitative methods for business decisions explores simplex method for solving linear programming model. Through a review of relevant, scientific literature, the simplex method and its application in solving linear programming problems are investigated. In the theoretical part, a fundamental terminological distinction is given, related to significant concepts in the paper. An example is presented in the practical part (research results). The production company had two production programs that produced two types of concrete blocks (A and B). The solution was first reached by analytical optimization, i.e. the simplex method. The solution was then checked in Excel, using the Solver add-in. It is also evident that the computer program Excel uses the simplex method to solve the problem of linear programming. The optimal production program is 27.4 blocks of the first type (A) and 28.6 blocks of the second type (B). At the same time, net profit was maximized and amounted to 584,077 monetary units (MU). All restrictions regarding the availability of materials (aggregates and cement) are fully met. In the case of the last restriction (working hours), 7.8 hours remained unused. The Goal Seeking analysis was also considered below, with the set goal of making a net profit of 600,000 monetary units. Ultimately, the methods, techniques, and tools covered by operational research have an indispensable application in today’s business environment, making it easier for managers and employees to improve productivity and efficiency and achieve successful results.