ICS Part 2 Mathematics Chapter 5 Short Questions Preparation

Check whether the region of graph 2x + 3y > 1 lies on the origin side or not.

• Ans 1: The graph of 2x + 3y > 1 is an open half plane.
  As 2(0) + 3 (0) > 1 is not true.
  So the region is not on the origin side.

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State fundamental extreme point theorem.

• Ans 1: From all the points in a plane bounded by a number of lines the maximum or minimum value of the objective function occurs only at one of the vertices of the bounded linear region.

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Define convex region.

• Ans 1: if the line segment obtained by joining any two points of a region lies entirely within the region, then the region is called convex.

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State fundamental extreme point theorem.

• Ans 1: From all the points in a plane bounded by a number of lines the maximum or minimum value of the objective function occurs only at one of the vertices of the bounded linear region.

Define optimal solution

• Ans 1: The feasible solution, which maximizes or minimizes the objective function, is called the optimal solution.

Define problem constraints.

• Ans 1: The system of linear inequalities involved in the problem concerned is called problem constraints.

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Define an objective function.

• Ans 1: A function, which is to be maximized or minimized, is called an objective function.

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Define convex region.

• Ans 1: if the line segment obtained by joining any two points of a region lies entirely within the region, then the region is called convex.

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Define decision variables.

• Ans 1: The variables used in the system of linear inequalities relating to the problems of everyday life are non-negative are called decision variables.

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Define non-negative constraints and decision variable.

• Ans 1: The variables used in the system of linear inequalities relating to the problems of everyday life non-negative are called non-negative constraints. The non-negative variables are called decision variables.

Define convex region.

• Ans 1: if the line segment obtained by joining any two points of a region lies entirely within the region, then the region is called convex.

Define a corner point.

• Ans 1: A point of a solution region where two of its boundary lines intersect is called a corner point or a vertex of the solution region.

Define a feasible solution set.

• Ans 1: A set containing of all the feasible solution of the system of linear inequalities is called a feasible solution set.

What are constraints in linear programming ?

• Ans 1: The conditions in the form of linear equations and in-equations are known as constraints.

Define optimal solution

• Ans 1: The feasible solution, which maximizes or minimizes the objective function, is called the optimal solution.