# Objective function of a linear program with multiple variables.

• MHB
• Yassineon
In summary, the objective function of a linear program is the function that is being minimized or maximized. In this case, the function is represented by the formula (MIN(lambda)wj), which aims to minimize the weighted sum of the variables with weights determined by lambda. This is a common objective function in linear programming, used to minimize cost or maximize profit.
Yassineon
Hello,
Please I need help to find the objective function of a linear program (attachement : example).
I tried to figure it out from the formula provided in (attachement : formula) but I couldn't understand it, it's written (MIN(lambda)wj) I think it's the key to resolve my question ! ( Full file is attached too )
Any help as little as it could be, would be most welcomed!

#### Attachments

• Formula (page 6).PNG
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• Example (Page 9).PNG
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Hello,

The objective function of a linear program is the function that you are trying to minimize or maximize. In this case, the objective function is represented by the formula (MIN(lambda)wj). Let's break it down to understand it better.

- MIN(lambda) represents the minimum value of lambda, which is a variable in the problem.
- wj represents the weight of each variable j in the problem.

So, the objective function is trying to minimize the weighted sum of the variables, where the weights are determined by the value of lambda. This is a common objective function in linear programming, where the goal is to minimize the cost or maximize the profit.

I hope this helps. If you have any further questions, please don't hesitate to ask. Good luck with your linear program!

## 1. What is an objective function in a linear program?

An objective function in a linear program is a mathematical expression that represents the goal or objective of the program. It is typically a linear combination of the decision variables and is used to maximize or minimize a specific quantity, such as profit or cost.

## 2. How is an objective function determined in a linear program with multiple variables?

The objective function in a linear program with multiple variables is determined by identifying the desired outcome or goal of the program and then formulating a mathematical expression that represents it. This expression should be a linear combination of the decision variables and should be either maximized or minimized.

## 3. What is the role of the objective function in a linear program?

The objective function plays a crucial role in a linear program as it defines the goal or objective of the program. It helps to guide the decision-making process by providing a measurable and quantifiable target that the program aims to achieve.

## 4. Can an objective function have multiple variables?

Yes, an objective function in a linear program can have multiple variables. This is often the case in real-world problems where there are multiple factors or variables that need to be considered in order to achieve the desired outcome.

## 5. How is the optimal solution of a linear program determined using the objective function?

The optimal solution of a linear program is determined by finding the values of the decision variables that satisfy the constraints and maximize or minimize the objective function. This can be done using various methods, such as graphical methods, the simplex method, or other optimization algorithms.

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