Business Mathematics | Unit-5 linear programming Notes and Problems with solutions | 4th sem CBCS Pettern Guahati University


UNIT : 5 Linear Programming

Meaning of linear programming:

The problem of optimizing (ie maximizing or minimizing) a linear function subject to a set of linear restrictions (restraints or constraints) as well as non-negativity restriction is called a linear programming problem i.e. LPP. The function to be optimized is called the objectivefunction. 


Solution of LPP: Solution values of decision variables Xj(j=1,2,...,n) which satisfy the constraints of a general LPP is called the solution to that LPP.

Feasible Solution: Solution values of decision variables Xj(j=1,2,...,n) which satisfy the constraints and non-negativity conditions of a general LPP are said to constitute the feasible solution to that LPP. Basic Solutions: for a set of m equations in n variables (n > m) a solution obtained by setting (n - m) variables equal to zero and solving for remaining m equations in m variables iscalled a basic solution.

Basic Feasible Solution: A feasible solution to an LPP which is also the basic solution is called the basic feasible solution. basic feasible solutions are of two types:

(a) Degenerate: A basic feasible solution is called degenerate if at least one variable possesses zero value. 

(b) Non-degenerate: A basic feasible solution is called non-degenerate if all m basic basic variables are non-zero and positive. Optimum Feasible Solution: A basic feasible solution which optimises the objective function of the given LPP is called an optimum feasible solution.

Q1. Write the use of linear programming. 

Ans:Linear programming is one of the most important and most popular quantitative tools used in Operation Research. It is widely applied in several functional areas of business such as production, finance, marketing, distribution, advertising, administration, defence etc.

Q2. Write the limitation of linear programming

Ans: The limitation of linear programming are as follow: (i) In order to apply linear programming (LP) technique, the objective function and the constraints must be expressed linearly. (ii) In order to apply LP technique, the co-efficients in the objective function and the constraints must be completely know and they must not change during the period of study.

(iii) To apply LP technique there must be only one goal which is expressed in the objective function like maximizing the value of the profit function or minimizing the cost function. Linear programming will fail to give a solution if management has multiple goal.

Q3. Write the method of solving Linear Programming problems. 

Ans : The method of solving Linear Programming problems are

(a) Graphical Method (b) Simplex Method

Q.4. What are the assumptions of linear Programming?

Ans : The following four assumptions are made in the Linear Programming Problems:

1. Linearity: The amount of resource required for a given activity is directly proportional o the level of the activity. All relationship in the Linear Programming model, i.e., in both objective function and constraints must be linear.

2. divisibility: The solution values of the decision variables and resources can take any non-negative values, ie, the fractional values of the decision variables are permitted. 3. Certainty: All the coefficients in the objective function and constraints are completely known with certainty and do not change during the period being stated.

4. Additivity: The total output for a given combination of activity levels is the algebraic sum of the output of each individual process.


Unit-2 Calculus I

Unit-3 Calculus II


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