Problem 25 - Algebra and Trigonometry

Question

What is an objective function in a linear programming problem?

Step-by-Step Solution

Answer

In a linear programming problem, an objective function is the function that needs to be optimized (maximized or minimized). It quantitatively represents the goal of the problem, in terms of decision variables.

Step 1: Define Linear Programming

Linear programming is a mathematical optimization technique for a system of linear constraints and a linear objective function.

Step 2: Introduce Objectives

Linear programming problems often involve an objective, which is the goal an organization or individual wants to achieve. This can be maximizing profit, minimizing cost, or reaching a specific operational level.

Step 3: Explain the Objective Function

The objective function quantifies the objective, representing it as a mathematical equation. In a linear programming problem, the decision variables in this equation are manipulated to find the optimal solution. For instance, if an organization aims to maximize profit, the objective function might be the total revenue minus total cost. The task is to manipulate the variables that affect profit (like production levels) so as to maximize this function.