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Chapter 5: Problem 25

What is an objective function in a linear programming problem?

Short Answer

Expert verified
An objective function in a linear programming problem is a function composed of decision variables that the problem seeks to optimize, either maximized or minimized, subject to certain constraints. It's typically represented as a mathematical equation.

Step by step solution

01

Definition of Objective Function

An objective function in a linear programming problem is a function that the problem seeks to optimize. It is typically represented as a mathematical equation composed of decision variables.
02

Role of Objective Function

The main role of an objective function is to be optimized, either maximized or minimized, subject to certain constraints. For example, in business or economics, an objective function can be used to maximize profit or minimize cost, given certain resources or constraints.
03

Mathematical Representation of Objective Function

An objective function is often represented as \(f(x,y)\) or \(z = ax + by\), where \(x\) and \(y\) are the decision variables, and \(a\) and \(b\) are constants. These constants represent the coefficients of the decision variables in the objective function.

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Most popular questions from this chapter

In Exercises \(5-18\), solve each system by the substitution method. $$ \begin{aligned} &x+y=6\\\ &y=2 x \end{aligned} $$

What does a dashed line mean in the graph of an inequality?

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Many elevators have a capacity of 2000 pounds a. If a child averages 50 pounds and an adult 150 pounts, write an inequality that describes when \(x\) children and\(y\) adults will cause the elevator to be overloaded. b. Graph the inequality. Because \(x\) and \(y\) must be positive, limit the graph to quadrant I only. c. Select an ordered pair satisfying the inequality. What are its coordinates and what do they represent in this situation?
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