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Linear programming is a modeling technique in resource allocation decisions (Render, Stair, Hanna, & Hale, 2019). Each linear programming problem will have an objective function that is seeking to either minimize or maximize some quantity. For example, the main objective of someone who wants to purchase a new television with a budget of $500 could be to minimize the cost being spent. With both maximization and minimization LP problems comes both similarities and differences when computing the two.
Similarities: In both minimization and maximization linear programming problems, we are able develop a graph using lines to represent the constraints, which will ultimately give us a region as a solution for the problem. This is known as the graphical solution for solving LP problems. We can also use the corner point method for either type of linear programming problem as well. The isoprofit line method is used for maximization problems, while the similar line method for minimization problems would be isocost line method. Both of these methods define a feasible region that will provide the optimal solution for each linear programming problem.
Differences: The most obvious difference between the two would be that maximization is when you are attempting to maximize the optimal solution while minimization you are attempting to minimize the optimal solution. Since both problems can be bounded, the difference between the two is that using the isoprofit line method in the maximization linear programming problems, the optimal solution would be bounded in the upper right while using the isocost line method in the minimum linear programming problems, the optimal solution would be bounded to the lower left. To put it in perspective, it only makes sense that when maximizing you are father from zero, while minimizing is closer to zero.
Render, B., Stair, R. M., Hanna, M. E., & Hale, T. S. (2019). Quantitative analysis for management. In Quantitative Analysis for Management (13th ed.). essay, Pearson.