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Linear programming is a numerical strategy that permits deciding the most ideal result or arrangement from a given arrangement of boundaries or a bunch of necessities. The fundamental benefit of linear programs is that it assists with performing demonstrating or reenactment to track down the best arrangements as per the accessible cash, energy, assets, time, space, and other related components or factors. (Lithmee, 2019). There are seven requirements for Linear programming; understand a problem, one objective function, one or more constraints, alternative courses of action, objective function and constraints are linear—proportionality and divisibility, certainty, divisibility, and nonnegative variables. A linear program can fail to have an optimal solution if the feasibility region is unbounded. The two minimization linear programs we examined had unbounded feasibility regions. The feasibility region was bounded by constraints on some sides but was not entirely enclosed by the constraints. Both minimization problems had optimal solutions. If we were to consider a maximization problem with a similar unbounded feasibility region, the linear program would have no optimal solution (Sekhon & Bloom, 2021).
Similarities: Both minimization and maximization use both the graphical solutions approach and corner point method to identify a set or region. The graphical method works only when there are two decision variables, but it provides valuable insight into how larger problems are structured. Graphical solutions are invaluable in providing us with insights into how other approaches work. When there are more than two variables, it is not possible to plot the solution on a two-dimensional graph, and we must turn to more complex approaches (Render et al., 2019). The corner point method is simpler conceptually than the isoprofit line approach, but it involves looking at the profit at every corner point of the feasible region because a solution will lie on one or more corners. Maximization can be used by the isoprofit line solution method and the minimization problems can use the isocost line solution method (Render et al., 2019).
Differences between minimization and maximization problems; For maximization, the Isoprofit line solution method is to track down an ideal arrangement with the most noteworthy benefit need not register the expense at each corner point yet rather draw a progression of equal expense lines. The ideal arrangement is the point lies in the plausible locale that delivers the most elevated benefit. The lowest cost line (i.e., the one closest to the origin) to touch the feasible region provides us with the optimal solution corner. The difference is that in minimization problems, the best isocost line is that closest to the zero origins and the region must be bounded on the lower left. In maximization problems, the best profit line is the one farthest from the zero origins and it must be bound on the top and to the right. A difference between minimization and maximization problems is that: minimization problems cannot be solved with the corner-point method (Sekhon & Bloom, 2021).
Lithmee. (2019, January 3). What is the difference between linear and nonlinear programming. https://pediaa.com/what-is-the-difference-between-linear-and-nonlinear-programming/
Sekhon, R., & Bloom, R. (2021, January 2). 3.2: Minimization applications. https://math.libretexts.org/Bookshelves/Applied_Mathematics/Applied_Finite_Mathematics_(Sekhon_and_Bloom)/03%3A_Linear_Programming_-_A_Geometric_Approach/3.02%3A_Minimization_Applications
Render, B., Stair, R. M., Hanna, M. E., & Hale, T. S. (2016). Quantitative analysis for management. In Quantitative analysis for management (p. 14). New York, NY: Pearson.