Linear Programming

Linear Programming:Let us understand about Linear Programming.Linear Programming is the universal method of most favorable part of limited wherewithal such as labor, substance, engine, resources etc., to quite a few competing behavior such as goods, services, jobs, projects, etc, on the fundamentals of known criterion of optimality.Now let us see what we mean by linear programming constraints.The linear inequalities or equations on the variables of a linear programming problem are called constraints. The conditions x >- 0, y >- 0 are called non-negative restrictions.Lastly let us see one example problem of linear programming.Let us solve linear programming.Example problem:

Solve:

Minimize: 4a + 5b + 6c

Here we can see the method of solving linear programming.

a + b >= 11

a - b <= 5 c - a - b = 0 7a >= 35 - 12b

a >= 0 b >= 0 c >= 0

Solution:

Step1: We use the equation c-a-b=0 to put c=a+b (>= 0 as a >= 0 and b >= 0) and so the linear

Programming is reduced to minimize.

=4a + 5b + 6(a + b)

=4a + 5b + 6a +6b

= 10a + 11b

Subject to

a + b >= 11

a - b <= 5 7a + 12b >= 35

a >= 0 b >= 0

The minimum occurs at the intersection of a - b = 5 and a + b = 11

This is the first step in solving linear programming.

Step2: The second step in solving linear programming involves the following step

By using Elimination method we can get the value of a = 8 and b = 3

To find the C value (substitute a and b value in c= a + b ) c = 11

The value of the objective function 10a + 11b = 80 + 33 = 113.

Thus these are the steps involved in solving linear programming.