Problem 25
Question
What is an objective function in a linear programming problem?
Step-by-Step Solution
Verified Answer
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.
1Step 1: 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.
2Step 2: 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
3Step 3: 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.
Other exercises in this chapter
Problem 24
In Exercises \(19-30,\) solve each system by the addition method. $$ \left\\{\begin{array}{l} 2 x-7 y=2 \\ 3 x+y=-20 \end{array}\right. $$
View solution Problem 24
Let \(x\) represent the first number, \(y\) the second number, and \(z\) the third number. Use the given conditions to write a system of equations. Solve the sy
View solution Problem 25
write the partial fraction decomposition of each rational expression. $$ \frac{x^{2}+2 x+7}{x(x-1)^{2}} $$
View solution Problem 25
Graph each inequality. $$y \geq \log _{2}(x+1)$$
View solution