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Linear programming

Chapter Three

FOR ONLINE READING ONLY
Linear programming

Introduction

Most production companies and industries aim at optimization of profit in
such a way that operational costs are minimized in order to maximize profit.
Linear programming is a mathematical method used to determine the best
possible outcome in problems that can be modelled by using linear equations
and inequalities. In this chapter, you will learn about formulation of linear
programming problems, constraints, and objective functions. You will also
learn about optimal and graphical solutions of linear programming problems.
The competencies developed will help you to decide, allocate, select, schedule,
and evaluate resources for the purpose of optimizing the output especially
in the fields of agriculture, business, engineering, energy, manufacturing,
transportation, and many other fields.

Think
Decision-making in production companies without knowledge of
linear programming. products of type A and type B per month,

Formulation of linear programming For instance, if a company manufactures
Mathematics for Secondary Schools Formulation of a linear programming then the decision variables can be defined
problems

as follows:
problem involves interpretation of a
Let x be the number of units of product
verbal description of the problem into
of type A and y be the number of units
algebraic equations or inequalities.
of product of type B manufactured per
It requires identification of decision
month.
variables, an objective function, and
constraints.
The constraints of a linear programming
Decision variables
problem are inequalities or equations
Decision variables are unknown Constraints
which connect the decision variables
quantities that decide the output. They under certain restrictions or limitations
are a set of quantities that need to be of resources. For instance, px qy+ ≤ r
determined in order to solve the problem. is a constraint for a maximization problem

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