Typically when you hear the word "programming," you may think of a computer program or coding within technologies. Linear programming, however, has very little to do with computer programming and has more to do with mathematical programming. You will often see linear programming used through the worlds of finance, marketing, accounting, and even in the military. When using linear programming, all problems will look to either maximize or minimize a quantity of some sort, usually profits or cost$.$ There are several similarities and differences with linear programming, regardless of the outcome desired.

Linear programming has an objective function whether you are looking to minimize or maximize constraints. This objective function is the property that is the focus of being either minimized or maximized within the problem. In some cases, a company may look to maximize their profits by using linear programming. In an example of minimization, another company may want to decrease their overtime costs. Another similarity that linear programming has when minimizing or maximizing some quantity are the presence of constraints, or restrictions. These restrictions limit the degree in which the objective can be pursued. When using linear programming, a company may be reviewing to increase their profits by manufacturing an increased inventory. However, the company may not have the amount of staff or machines that are necessary for this maximization. Overall, the objective function will be restricted by constraints that need to be identified. Linear programming has an end goal of finding a solution, whether that be a minimized or maximized result.$$

Although there is a decent amount of similarities within linear programming, there are also differences between the minimization and maximization problems. When using minimization problems, the end goal that is desired is to find the smallest possible value of the objective function. On the contrary, maximization problems look to identify the opposite in finding the largest possible value. The constraint values will also differ from minimization to maximization, as the values and outcomes will not look the same. Depending on the linear programming, constraints will need to be evaluated to fit into the desired result. Whether you are using linear programming for minimization or maximization, the interpretation will also look different as the end result will either need to be the highest or the lowest based on what problem is used. The objective function can be changed as needed to fit the outcome and alter the linear programming.

Both maximization and minimization problems used in linear programming are there to help businesses, companies, or even individuals identify ways to expand a specific quantity that is desired. This could be to increase profits or inventory, or reduce overtime and shipping costs. Using these problems helps to find the extreme on either end, and can guide you to the best possible outcome. Many different lines of business can use linear programming as it is not restrictive just to the world of finance or business. The approach that is taken can be tailored to the needs of the individual, and is not completely structured to one industry.