Question about linear programming

In summary, the conversation discusses three linear equations y1, y2, and y3, with y1= ax+b, y2=mx+k, and y3=n, where a, b, m, k, and n are constants. It is assumed that all three equations intersect at y1=y1=y3=n. The question is whether the area between the curves y1 and y2, from 0 to the intersection, represents anything useful in economics. This area is commonly referred to as the "feasible region" and its size can be computed to provide useful information in certain applications.
  • #1
homomorphism
19
0
basically, let's say i have three linear equations, y1, y2, and y3.

assume y1 = ax+b where a and b are constants
assume y2 = mx+k where m and k are constants
assume y3 = n where n is a constant

also, now assume that they all intersect at y1=y1=y3=n.

would the area between the curves, y1 and y2, from 0 to the intersection represent anything? I've attached a sample pic for reference.

View attachment linear area.bmp
 
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  • #2
Wow, I think I repeating what I just said in the previous thread! What anything in mathematics "represents" depends upon the specific application. In economics that area is commonly referred to as the "feasible region" because it is, by the terms of the application that gives you those equations, the area in which a solution must occur.
 
  • #3
well...i know it's the feasible region. But let's stick with the economics example...does computing the actual size of that region give anything useful?
 

What is linear programming?

Linear programming is a mathematical method used to optimize a linear objective function, subject to linear equality and inequality constraints. It is often used to find the best solution to a problem with multiple variables and constraints.

What are the main components of a linear programming problem?

The main components of a linear programming problem are the objective function, decision variables, and constraints. The objective function represents the goal or objective of the problem, while the decision variables are the values that can be changed to reach the optimal solution. Constraints are the limitations or requirements that must be met in order to find the optimal solution.

What are some real-life applications of linear programming?

Linear programming has many practical applications, such as in supply chain management, production planning, and resource allocation. It is also used in economics, finance, and engineering to optimize processes and maximize efficiency.

What is the difference between a feasible and an optimal solution in linear programming?

A feasible solution is one that satisfies all of the constraints in a linear programming problem. An optimal solution is a feasible solution that also maximizes or minimizes the objective function. In other words, it is the best possible solution to the problem.

What are the limitations of linear programming?

Linear programming is based on certain assumptions, such as linearity and certainty, which may not always hold true in real-world problems. It also requires a well-defined and consistent objective function and constraints. Additionally, it can become computationally complex and time-consuming for large-scale problems.

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