Profit Optimization and Production of Maesa Cake and Bakery Shops with Linear Programming-Simplex Method

Omah Jenang is one of the industries engaged in the production of traditional snacks. Currently Omah Jenang does not yet have guidelines for realizing the formation of the composition of production quantities correctly based on calculations that still use forecasting methods. Therefore Omah Jenang often experiences difficulties in providing raw materials and determining maximum profits. The purpose of this study was to de-termine the optimum yield of profits at Omah Jenang by using the simplex method linear program with the help of Lindo Software. The data used is food production data at the Omah Jenang Home Industry in 2022. The method used in this study is the Linear Pro-gramming simplex method and the Lindo Software application. The results of optimization calculations using the linear programming method and the help of Lindo Software are that the maximum profit in a month is IDR 20,000,000 in producing 800 packages of madumongso. Based on the calculation results it can be concluded that the benefits obtained by using the simplex method with the help of Lindo Software can be obtained maximum results.

In current conditions, many people are competing to set up businesses to meet their daily living needs. One of the various ways to improve people's welfare is through small and medium enterprises (SMEs). As many businesses develop and are accompanied by intense competition, many problems will arise and will affect the profits of SMEs. The problem that occurs at UKM Pie Bu Sri is the problem of calculating the optimum profit obtained every day from the production of its activities. The aim of this research is to help calculate the optimum profit for UKM Pie Bu Sri so that it can be done accurately and quickly. In order to achieve this goal, the Simplex Linear Programming Method and QM for Windows Software were used to find the optimum profit estimate obtained in each production activity carried out by UKM Pie Bu Sri within a period of one day. The results of the maximization calculations show that in order to achieve maximum profits, Mrs. Sri must make 60 Brownie Pies and produce 25 Fruit Pies with a profit of IDR 99,500 per day.

The current research shows how to utilize the linear programming to perform a profit maximization on two economic cases and analyze the sensitivities of the obtained solutions to identify the key factors influencing the solution, which then can be used as the basis to decide the most profitable business. The case of the current study is identifying the most profitable project of two housing developments in Indonesia. The linear programming of the simplex method is applied to address the problem. The findings indicate that the linear programming solution and its sensitivity analysis effectively and efficiently inform and assist businessmen in identifying the most profitable project under the given constraints. In this case, the linear programming with its sensitivity analysis asserts that selecting a business activity based merely on the amount of its apparent profit may lead to an improper business decision. An example from the current study shows that although the second project yields a higher profit, the solution of the linear programming suggests that the first project is more relevance to its market demand and it needs less capital than that the second project. The higher profit obtained of the second project tends to be relative or fictitious since both projects result in the same return on investment (ROI). Moreover, the sensitivity analysis indicates that the optimization solution of the first project is more stable to change than that of the second project. Keywords: Profit Optimization, Return on Investment, Market Demand, Sensitivity Analysis, Simplex Method DOI: 10.7176/EJBM/11-19-06 Publication date:July 31st 2019

Time Preference, Firm Growth, and Programming Models††Research on this topic was supported in part by a grant from the Halliburton Education Foundation.

The growth of micro, small and medium enterprises (UMKM) makes business actors want to optimize profits. The limitations of raw materials and resources encourage business actors to review their strategies in order to generate optimal profits. The main purpose of the study is to calculate the optimal profit from the banapuff business and provide business strategic recommendations for the combination of products produced in order to generate optimal profits. The calculation of optimal profit will use linear programming with the simplex method, because the simplex method can confuse optimization calculations with many variables and constraints. The results of the study show that UMKM businesses can increase production profits by RP380,000.00 per production with the provision of producing 57.5 puffed bananas, 12.5 chocolate bananas and 20 sesame chocolate bananas. With this result, it is hoped that business actors will get a new business strategy in the efficiency of raw materials and the combination of product production through a systematic approach.

The k-means method is a widely used technique for clustering points in Euclidean space. While it is extremely fast in practice, its worst-case running time is exponential in the number of data points. We prove that the k-means method can implicitly solve PSPACE-complete problems, providing a complexity-theoretic explanation for its worst-case running time. Our result parallels recent work on the complexity of the simplex method for linear programming.

A basis-deficiency-allowing variation of the simplex method for linear programming

Chamfer distances on the isometric grid are considered. A new method to compute the chamfer distances based on linear optimization is presented. In the LP model the starting pixel is the Origin, that is a triangle of the grid having co-ordinates (0, 0, 0). The co-ordinates of the end pixel of the path give the right-hand side of the model. The variables are the used numbers of the elementary steps. Each type of an elementary step has a uniquely defined weight. Our operational research approach determines the optimal paths as basic feasible solutions of a linear programming problem. We give directed graphs with feasible bases as nodes and arcs with conditions on the used weights such that the simplex method of linear programming may step from one feasible basis to another feasible basis. Thus, the possible course of the simplex method can be followed and the optimal bases can easily be captured. Thus, the final result of the analysis is an O(1) checking of the feasibility and optimality conditions. The optimal bases are summarized in a theorem which is the consequence of the general theory of linear programming. The method can be applied for other grids, but it needs to be adjusted for the particular grid.

The simplex method for linear programming is known to be highly efficient in practice, and understanding its performance from a theoretical perspective is an active research topic. The framework of smoothed analysis, first introduced by Spielman and Teng (JACM ’04) for this purpose, defines the smoothed complexity of solving a linear program with d variables and n constraints as the expected running time when Gaussian noise of variance σ2 is added to the LP data. We prove that the smoothed complexity of the simplex method is O(σ−3/2 d13/4log7/4 n), improving the dependence on 1/σ compared to the previous bound of O(σ−2 d2√logn). We accomplish this through a new analysis of the shadow bound, key to earlier analyses as well. Illustrating the power of our new method, we use our method to prove a nearly tight upper bound on the smoothed complexity of two-dimensional polygons.

For many of us, modern-day linear programming (LP) started with the work of George Dantzig in 1947. However, it must be said that many other scientists have also made seminal contributions to the subject, and some would argue that the origins of LP predate Dantzig’s contribution. It is matter open to debate [36]. However, what is not open to debate is Dantzig’s key contribution to LP computation. In contrast to the economists of his time, Dantzig viewed LP not just as a qualitative tool in the analysis of economic phenomena, but as a method that could be used to compute actual answers to specific real-world problems. Consistent with that view, he proposed an algorithm for solving LPs, the simplex algorithm [12]. To this day the simplex algorithm remains a primary computational tool in linear and mixed-integer programming (MIP). In [11] it is reported that the first application of Dantzig’s simplex algorithm to the solution of a non-trivial LP was Laderman’s solution of a 21 constraint, 77 variable instance of the classical Stigler Diet Problem [41]. It is reported that the total computation time was 120 man-days! The first computer implementation of an at-least modestly general version of the simplex algorithm is reported to have been on the SEAC computer at the then National Bureau of Standards [25]. (There were apparently some slightly earlier implementations for dealing with models that were “triangular”, that is, where all the linear systems could be solved by simple addition and subtraction.) Orchard-Hays [35] reports that several small instances having as many as 10 constraints and 20 variables were solved with this implementation. The first systematic development of computer codes for the simplex algorithm began very shortly thereafter at the RAND Corporation in Santa Monica, California. Dantzig’s initial LP work occurred at the Air Force following

Linear programming is a mathematical method for choosing the best product combination to maximize profit or decrease cost within the limitations of available resources. In this article, we have proposed the linear programming application for profit Maximization of a Biscuit Factory in Bangladesh. For linear programming problems, the Simplex algorithm provides a powerful computational tool, able to provide fast solution to very large-scale application. The optimization principal examined unit cost of production, the selling price and the quantity of different raw materials used in production. A model for the problem was formulated and optimum results derived using software that employed simplex method. Our main goal is to emphasize the uniqueness of linear programming modeling at the business level as an optimization technique, and to encourage manufacturing companies to employ linear programming to determine their optimal profit.

The full use of resource capacities of agricultural enterprises favorably affects the general increase in economic efficiency and rational production making them more competitive in the market. This creates the need for constant improvement of business strategies that uses all available resources to create the most profitable production. The main objective of this study was to find the ideal structure of production in agricultural enterprise and to enable the realization of maximum profit using the available production resources (land, mechanization, labor forces). As the basic method of planning, this study used the simplex method of linear programming which gives the most profitable sowing structure after detailed analysis of resources and achieved results, based on the limitations and gross margin. This work showed that the use of modern methods in production planning is one of the cheapest and safest methods for development of agricultural enterprises.

The processes of optimization of the production plan according to certain criteria by modeling were investigated. Achieving effective results directly depends on the optimal production plan. The most important thing in determining the optimal production plan is the choice of modeling criteria. For the most part, the quality of decisions is characterized not by one but by many incomparable criteria. Therefore, it is necessary to make decisions based not on one but on many criteria. This so-called multi-objective optimization problem. For solving such problems is widely used mathematical methods. Mathematical approach can be used to solve problems in any particular activity as mathematics abstracted from specific features characteristic of a particular solution. Therefore, from the point of view of mathematics, the optimal result can be obtained with various established criteria, but from the economic point of view it is important to choose the ones that are of decisive importance. That is, their weight is important for the consumer when making a purchase decision, and for the manufacturer – in terms of production capabilities of certain types and results (production efficiency). The basis of the operation of any enterprise is a production program (production and sales plan). The main task of the production plan is to meet the needs of consumers in high-quality products, which are produced with the best use of resources, on the one hand, and the enterprise to get the maximum profit, on the other. With this in mind, a two-criteria optimization model that allows to make a production plan was proposed. The plan ensures that products are produced with the best use of available resources and at the same time ensures maximum quality of manufactured products and maximum profit from sales of these products. The solution of the problem with two objective functions and linear constraints is achieved by step-by-step solution of the proposed mathematical model of optimization of the production plan using the method of sequential restrictions. The simplex method was also used. An example shows an algorithm for solving the optimization problem.

Linear programming is a planning technique that uses mathematical models with the aim of finding the best product combinations in preparing an allocation of limited resources in order to achieve goals that are used optimally Sofjan Assauri (Hermawan, 2016). The simplex method is an approach in solving linear programming problems that have two or more decision variables where determining the optimal combination is done through repeated iterations of the simplex table until the optimum value is found in the optimization problem which includes maximizing profits or minimizing costs. The martabak home industry is one of the businesses operating in the culinary sector. One of the problems faced by the Martabak 88 home industry is determining the optimum production amount so as to obtain maximum profits. Therefore, a method is needed to determine the right combination of products made and the combination of products produced. The simplex method is the method used in this research to estimate the maximum profit obtained from sweet martabak and egg martabak.

In the previous chapter, the basics of the simplex and revised simplex algorithms were developed. Degeneracy and convergence issues were addressed. In this chapter we continue with several enhancements to the basic algorithm and related issues. In Section 6.2 we continue the development of sensitivity analysis which was first discussed in Chapters 2 and 3. We show that an analysis of the simplex tableau provides dual variable values, reduced costs and range analysis for the right hand side and objective function, but the simplex algorithm does not provide results which are as reliable as those obtained using projection and inverse projection. In Section 6.3 we develop the dual simplex algorithm. This is the simplex algorithm applied to the dual problem but using the primal simplex tableau. In our earlier development of the simplex algorithm we assumed that all variables had a lower bound of zero and an upper bound of oo. In Section 6.4 we show how to incorporate variables with arbitrary lower and upper bounds into the simplex algorithm. The simplex algorithm requires an initial feasible basis. In Section 6.5 we show how to find an initial basic feasible solution. In Step 3 of the simplex algorithm it is necessary to select a variable to enter the basis. In Section 6.6 we describe several methods for selecting the entering variable. In Section 6.7 we discuss other numerical issues such as tolerances, the minimum ratio test and scaling. Concluding remarks are given in Section 6.8. Exercises are provided in Section 6.9. One topic not covered in this chapter is preprocessing. By preprocessing we mean analyzing the problem prior to solution in order to discover obvious redundancies, tighter variable bounds, eliminate variables and constraints, etc. This is very important in reducing the solution time for solving linear programs. Our discussion of preprocessing linear programs is postponed until Chapter 15.