Profit Optimization using a Linear Programming Model

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