By taking the help of Linear Programming Calculator, you will get the exact solution quickly. You have to provide all your conditions and functions as input in the respective fields and press the calculate button to get the answer in seconds.

**Linear Programming Calculator: ** Learn the procedure to solve the linear programming of the given constraints. Our free handy linear programming calculator tool is designed to help people who want to escape from mathematical calculations. One who is willing to know the detailed process involved in solving the Linear Programming of a function can read the further sections of this article.

## How to Solve Objective functions with Linear Constraints?

Here, you can see the simple guidelines to solve the objective function with the given linear constraints. Follow these steps and compute the maximum and minimum of the functions.

- Take any objective function P and other linear constraints
- Out of all the constraints, compute the conditions which are having two variables for example x and y
- Convert the expression as bring one variable y
- By taking the slope of those constraints draw a graph
- Mark the feasible region and find out the vertices
- Substitute all the values of vertices in the objective function
- Check for which vertices, the function is minimum and maximum

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**Example**

**Question: Find the feasible region for 2x+y=1000, 2x+3y=1500, x=0, y=0 and maximize and minimize for the objective function 50x+40y?**

Answer:

Given that,

Objective function f(x,y)=50x+40y

Given constraints are

2x+y=1000, 2x+3y=1500, x=0, y=0

2x+y=1000

y=1000-2x

2x+3y=1500

3y=1500-2x

y=(1500-2x)/3

y=500-2x/3

The graph will be

The shaded area will be the feasible region in the above graph

The vertices are (0,500), (375,250), (500,0)

f(x,y)=50x+40y

Substitute the vertices in the objective function

f(0,500)=50*0+40*500=20,000

f(375,250)=50*375+40*250=28,750

f(500,0)=50*500+40*0=25,000

The minimum value is (0,500)

Maximum values are (275,250)

### FAQ’s on Linear Programming

**1. What is the process of linear programming?**

Linear programming is the process of taking various linear inequalities relating to some situation and finding the best value obtained under those conditions.

**2. What is the linear function and examples?**

Linear functions are graphs as a straight line format. The standard form of linear function is y=f(x)=a+bx. It has one dependent variable and one independent variable.

**3. What are the components of linear programming?**

The three different equalities or inequalities or components of the linear programming are decision variables, objective function and constraints.

**4. How can you solve the linear programming problem?**

Find out the feasible region for the constraints and decision variables. Point out the vertices, and substitute those values in the objective function to get the maximize and minimize values.

**5. How do you solve the maximum value in linear programming?**

If linear programming can be optimized, an optimal value will occur at one of the vertices of the region representing the set of feasible solutions.