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Chapter 5: Problem 25

What is an objective function in a linear programming problem?

Short Answer

Expert verified
The objective function in a linear programming problem is the function that needs to be optimized (either minimized or maximized). This function represents the main goal of the problem, such as minimizing costs or maximizing profits.

Step by step solution

01

Understanding Linear Programming

Linear programming is a method for determining a way to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships.
02

Defining an Objective Function

The objective function in a linear programming problem is the function that needs to be optimized (either minimized or maximized). This function represents the goal that you are trying to achieve
03

Role of Objective Function in Linear Programming

The objective function is one of the two main components of a linear programming problem, along with constraints. The objective function represents the quantity which needs to be minimized or maximized. For instance, it could represent the total cost of materials to be minimized, or the total profit to be maximized.

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Most popular questions from this chapter

write the partial fraction decomposition of each rational expression. $$ \frac{4}{2 x^{2}-5 x-3} $$

write the partial fraction decomposition of each rational expression. $$ \frac{x^{3}-4 x^{2}+9 x-5}{\left(x^{2}-2 x+3\right)^{2}} $$

write the partial fraction decomposition of each rational expression. $$ \frac{1}{x(x-1)} $$

Describe a situation in your life in which you would really like to maximize something, but you are limited by at least two constraints. Can linear programming be used in this situation? Explain your answer.

write the partial fraction decomposition of each rational expression. $$ \frac{a x+b}{(x-c)^{2}} \quad(c \neq 0) $$
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