Linear programming is a mathematical optimization technique used to find the maximum or minimum value of an objective function, subject to a set of constraints. In linear programming, the objective function and the constraints are all linear, meaning they are made up of linear combinations of variables.

Maximization and minimization are two common goals in linear programming. Maximization refers to the process of finding the maximum value of the objective function, while minimization refers to the process of finding the minimum value.

One key difference between maximization and minimization in linear programming is the direction of the objective function. In maximization problems, the objective function is set up such that an increase in the variables leads to an increase in the objective function. In minimization problems, an increase in the variables leads to a decrease in the objective function. This means that, in a maximization problem, we are looking for a combination of variables that leads to the highest possible value of the objective function, while in a minimization problem, we are looking for a combination of variables that leads to the lowest possible value.

Another difference between maximization and minimization in linear programming is the way in which the constraints are set up. In a maximization problem, the constraints are set up such that they limit the variables from taking on values that would lead to a higher objective function value. In a minimization problem, the constraints are set up such that they limit the variables from taking on values that would lead to a lower objective function value.

Overall, maximization and minimization in linear programming involve finding the maximum or minimum value of the objective function, subject to a set of constraints. The direction of the objective function and the way in which the constraints are set up are key differences between the two goals. Linear programming is a powerful tool that is used in a variety of fields, including economics, operations research, and engineering, to solve complex optimization problems.

## Discuss the similarities and differences between minimization and maximization problems using the graphical solution approaches of linear programming Â» StudyExcell

As with maximization problems, the opportunity loss can never be negative. Since the extreme value of the objective function always takes place at the vertices of the feasibility region, we identify the two critical points, 1, 3 and 4, 1. Alternatively we could use test point 4,6 , which also does not lie on any of the constraint lines. There is relationship when the profit increases and the cost price of the commodity. If it is Maximization-it means maximization of profits and in case of Minimization- it is meant to find minimum cost of production. Likewise, both have the same approach of developing a doable solution district by charting every one of the imperative lines. I asked my question because I did not know how you can check whether a function is minimizing or maximizing.

## 3.2: Minimization Applications

Follow the four steps to formulating LP problems on page 241. In this context, it refers to a planning process that allocates resourcesâ€”labor, materials, machines, and capitalâ€”in the best possible optimal way so that costs are minimized or profits are maximized. What is maximization in operation research? This has a maximum value of +1 and a minimum value of -1. Thus all the shading for the feasible region lies on the opposite side of the constraint lines from the point 0,0. Step by Step Solution Step I- Make a Table to create correct LP problem.