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Chapter 5: Problem 25

What is an objective function in a linear programming problem?

Short Answer

Expert verified
In a linear programming problem, the objective function is the expression that needs to be optimized (minimized or maximized). It represents the main goal of the problem in mathematical terms.

Step by step solution

01

Definition of Linear Programming

Linear programming is a mathematical method used for achieving the best outcome in a mathematical model. This method is valuable in a wide variety of fields like economics, military, and operations research. It involves optimization of a linear objective function, subject to linear equality and linear inequality constraints.
02

Objective Function

The objective function of a linear programming problem is the function that needs to be optimized (either minimized or maximized). This function is usually a linear function of the variables in the problem. In simpler terms, the objective function is the mathematical expression of the primary goal of the process under consideration. For instance, in an operations problem, this can be the amount of profit to maximize or the cost to minimize.
03

Examples of Objective Functions

For a more concrete understanding, consider this example: determine the number of units of each product to produce in order to maximize profits, given the cost, selling price, and availability of resources. The objective function in this case would be to maximize Profits = (Selling price - Cost) * Quantity. Here, the 'Quantity' of each product would be the variables of the objective function and the aim is to find the values of these variables that will maximize the profits. Similarly, in a cost minimization problem, an example of an objective function can be: Minimize cost = Constant + Variable cost * Quantity.

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Most popular questions from this chapter

Without graphing, in Exercises 73鈥�76, determine if each system has no solution or infinitely many solutions. $$\left\\{\begin{array}{l} (x+4)^{2}+(y-3)^{2} \leq 9 \\ (x+4)^{2}+(y-3)^{2} \geq 9 \end{array}\right.$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A system of two equations in two variables whose graphs are two circles must have at least two real ordered-pair solutions

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What is a constraint in a linear programming problem? How is a constraint represented?
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