Business Optimization: Linear Programming Model Report Analysis

This report presents a case study on profit optimization using a linear programming model for a chemical company in Ethiopia. The study focuses on maximizing profits by determining the optimal production levels of sulfuric acid and aluminum sulfate. The report begins by introducing the concept of linear programming and its relevance in business decision-making, emphasizing its role in resource allocation and efficiency. It then outlines the specific problem faced by the chemical firm, including the production constraints related to manufacturing processes and market demand. The report details the formulation of a linear programming model, including decision variables (sulfuric acid, aluminum sulfate), constraints (machine capacity, demand), and the objective function (profit maximization). The model is designed to be solved using Microsoft Excel's Solver, providing a practical approach to determining the optimal production mix. Finally, the report highlights the importance of this model in informing day-to-day business operations and making data-driven decisions. The report also references relevant literature on linear programming and its application in business and management science.

Profit Optimization using a linear Programming model
Business growth and sustainability is often dependent on the process of decision making. As
such, it is crucial that reliable tools are formulated to aid in the process of decision-making.
Examples of this tools include linear programming models which have been widely adopted in
the business world of today which is ever competitive. For instance, consider the case of scenario
of military strategies and planning whereby there is a question as to how men, weapons, and
other supplies can be distributed in such a way that is efficient. This clearly is a linear
programming problem which requires optimal allocation of resources.
As noted, the approach of linear programing then requires the use of, “a set of techniques and
methods inferred from mathematics and other sciences which can plan an efficient role in
impro4ing the management decisions” (Maurya, Misra, Anderson, & Shukla, 2015). Let us
consider a case in which an Ethiopian chemical firm sort to optimize their profit.
The problem and decision variables
Questions on whether a certain decision will be profitable to a firm in Ethiopia, have been for a
long time being determined by either the government or non-governmental bodies. It is therefore
crucial for a firm such as the chemical firm in this case to define new measures of decision-
making.
From historical data collection by the company, the company produces 51.5 tons of Sulphuric
acid daily and 40 tons of Aluminum Sulphate each day. The problem is to determine how much
to produce for the coming financial year.
In this problem, the company seeks to develop a product-mix linear program that optimizes the
firm’s profit. Decision variables are the thee mathematical symbols which represent the firm’s

activity levels (Anderson, Sweeney, Williams, Camm, & Kipp, 2012). Therefore, in our firm’s
problem, the decision variables include: Aluminum Sulphate, Sulphuric acid and any other
available resources. Further, 4 constraints are related with the number of machine for three for
three of the manufacturing processes (reaction, filtration, and evaporation). The demand factor is
used as an additional restriction on the amount that can be manufactured. Additional factors in
the model are profits per ton.
To obtain the coefficients the model’s constraints below are included in the linear programming
model which will be solved by Microsoft’s Excel Solver © which converts it into standard form:
The excel output will produce the standard solutions for the LP model after which it will be
translated to determine the optimal amount of Aluminium Sulphate and Sulphuric acid so as to
obtain the maximum possible profit per day depending on the market demand for the firm’s
product and thus inform the day to day business operations of the firm.

References
Anderson, D., Sweeney, D. J., Williams, T., Camm, J., & Kipp, M. (2012). An introduction to
Management science. In Quantitative Approaches to Decision Making (13th ed., pp. 55-
72). Boston: South-Western Cengage Learning.
Maurya, V. N., Misra, R. B., Anderson, P. K., & Shukla, K. K. (2015). Profit Optimization Using
Linear Programming Model A Case Study of Ethiopian Chemical Company. American
Journal of Biological and Environmental Statistics, 1(2), 51-57.