# Linear Programming

## Short Questions

Define Linear programming and Linear programming problem.

Linear programming: Linear programming is a mathematical technique of finding the maximum or minimum value of the objective function satisfying the given condition.

Linear programming problem: The problem which has the object of finding the maximum or minimum value satisfying all the given conditions is called linear programming problem (LPP).Define linear inequality.

Define boundary line with example.

In which condition the boundary line is dotted line?

Define Decision variables.

Define constraints with an example.

Define Feasible region and Feasible solution.

Feasible region: A closed plane region bounded by the intersection of finite number of boundary lines is known as feasible region. It is also called as convex polygonal region.

Feasible solution: The values of decision variables x and y involved in objective function satisfying all the given condition is known as feasible solution.What do you mean by objective function? Also write an example.

In an objective function (F) = 5x - 2y, one vertex of feasible region is (5, 2) then find the value of objective function.

Objective function, F = 5x - 2y

Vertex (x, y) = (5, 2)

Hence, F = 5(5) - 2(2) = 21

Which quadrants do the inequality x ≥ 0 and x ≤ 0 represent in a graph?

Which quadrants do the inequality y ≥ 0 and y ≤ 0 represent in a graph?

From the given inequality 4x + 3y ≥ 10, Write the boundary line equation.