# 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.

A relation represented by ax + by + c > 0, ax + by + c < 0, or ax + by + c ≥ 0 or ax + by + c ≤ 0 is known as the linear inequality in two variables x and y.

Define boundary line with example.

The Boundary line is the line which is the corresponding equation of given inequality and divides the coordinate graph into two halves. It is dashed for > and < and solid for ≥ and ≤. For example: the boundary line of inequality 5x - 8y ≥ 10 is 5x - 8y = 10.

In which condition the boundary line is dotted line?

The boundary line is dotted line if inequality contains > or < symbol.

Define Decision variables.

The non-negative independent variables involving in the L.P problem are called decision variables. For example: in 2x + 3y = 7, x and y are decision variable.

Define constraints with an example.

The conditions satisfied by the decision variables are called constraints. For example: if x and y be the number of the first two kinds of articles produced, then x + y ≥ 1000, x ≥ 0, and y ≥ 0 are the constraints.

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.

The linear function whose value is to be maximized or minimized (optimized) is called an objective function. For example: F = 4x - y, D = 5x - 6y.

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

Here,
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?

The inequality x ≥ 0 represent the first and fourth quartile and the inequality x ≤ 0 represent the second and third quartile.

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

The inequality y ≥ 0 represent the first and second quartile and the inequality y ≤ 0 represent the third and fourth quartile.

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

The boundary line equation of inequality 4x + 3y ≥ 10 is 4x + 3y = 10.