Page 1 of 11
European Journal of Business &
Social Sciences
Available at https://ejbss.org/
ISSN: 2235-767X
Volume 07 Issue 02
February 2019
Available online: https://ejbss.org/ P a g e | 537
A Study on Linear Programming and Its Usage in
Mathematics
Manju Sharma
Lecturer in Math G.S.S.S Bhatol (Hisar)
ABSTRACT
The usage of the linear programming can be observed in the stream lining.
A variety of operations and fields can be implemented with the help of the
linear programming. In most of the cases, the Simplex methodology is used
in relation with the linear programs so that the accuracy of the overall
results can be enhanced effectively.
In some cases, the processing of the linear programming can be done in
polynomial time so that the formulation of the given problem can be done
easily. Also, this linear programming is helpful in investing the normal
variants. Hence, linear programs can be used to find out the solutions form
the evaluation methods. A number of mathematical concepts are used in
linear programming. The current paper highlights the usage of linear
programming in Mathematics.
KEYWORDS:
Page 2 of 11
European Journal of Business &
Social Sciences
Available at https://ejbss.org/
ISSN: 2235-767X
Volume 07 Issue 02
February 2019
Available online: https://ejbss.org/ P a g e | 538
Linear, Programming, Evaluation
INTRODUCTION
The evaluations of the geometrical problems can be done easily with the
help of the linear programming where the terms like polynomials are
used to achieve the basic goal of yielding highly accurate results. Here,
the vertices diagrams and edges are used in association with the simplex
methods so that the final efficiency can be enhanced.
Also, in case of polynomials, these linear methods are allowed to execute
in efficient time. Here, the parameters of the polytope diagrams are used
to formulate the upper bound variables of the given polynomial where
width is supposed as an essential term for measurement and hence, the
process of evaluation is initiated.
In some cases, the determination of the actual values of the lower and
upper bound of a given polynomial can be performed through linear
programming with the evaluation of the edges and vertices of that
polynomial.
The general diagrams can be verified with the help of the Simplex method
having a type of self-double where the parameters of edges are pre- defined to precede the solution of the problem. In some cases, the edges
of the diagrams are used to evaluate the polynomial time for the
exponentially vertices. Hence, linear programming is proposed so as to
Page 3 of 11
European Journal of Business &
Social Sciences
Available at https://ejbss.org/
ISSN: 2235-767X
Volume 07 Issue 02
February 2019
Available online: https://ejbss.org/ P a g e | 539
execute the whole process in a sequence so that complexity of the
problems can be reduced.
Unbounded polyhedron is also used, in some cases; with the linear
programming for the purpose of verifying the linear imperatives. Here, all
the terms of the expression are made equal in order to simplify the
process of verification.
In case of the complex problems, the shadow-vertex method is used
where a variety of variables and functions are used in relation with the
linear programming to make the condition of the given problem easier to
evaluate.
Here, the property of top-down is used to simply a complex problem
where modules are formed to reduce the size of the main problem and if
the size of the obtained module is even large then these modules are sub- divided into the sub-modules and this process of decomposition of the
main problem into a number of modules and sub-modules continues
until the main problem becomes simpler. Hence, this concept of linear
programming makes them popular.
Flow charts are used in the linear programming where some basic
notations and representations are used to indicate the processing of a
problem where all the steps are performed in step-wise pattern. The
