INTRODUCTION TO LINEAR
PROGRAMMING (LP)
WHAT IS LINEAR PROGRAMMING
LP is a problem-solving
approach
developed
for
situations where we require to
determine
an
optimum
solution and where we face
certain
limitations
or
constraints on what we are
able to do. We may seek to:
• maximize profit
• minimize costs
• minimize travel time
The term
PROGRAMMING refers
not to the need for
computer programming
but to the fact that
technique comprises a set
of logical steps to
determine the optimal
solution to an LP problem.
The term LINEAR
ISOPROFIT LP GRAPHICAL METHOD
 The "isoprofit line solution method" is a graphical technique used in
linear programming to find the optimal solution by plotting lines
representing different levels of profit (isoprofit lines) within the
feasible region, where the point on the line that intersects the
feasible region at the highest profit level is the optimal solution; it's
primarily used for problems with only two decision variables due to
its visual nature.
CORNER POINT LP GRAPHICAL
METHOD
 The "corner point solution method" is a graphical technique used in
linear programming to find the optimal solution to a problem by
evaluating the objective function at each "corner point" (or extreme
point) of the feasible region, with the assumption that the optimal
solution will always lie at one of these corners; essentially, it
involves plotting the constraints, identifying the feasible region, and
then testing the objective function at each corner point to find the
maximum or minimum value depending on the problem objective. .
1. Alternate Optimal
Solution
When there are multiple
points on the feasible
region that provide the
same optimal value for
the objective function,
meaning
there
are
several equally "best"
solutions.
2. Infeasibility
When no combination of
FOUR
SPECIAL
CASES IN
LINEAR
PROGRAMMI
NG
20XX
An Infeasible Problem
maximize Z = 5x1 + 3x2
subject to:
The three constraints do not overlap to form a feasible
solution area. Because no point satisfies all three
constraints simultaneously, there is no solution to the
problem. Infeasible problems do not typically occur,
but when they do, they are usually a result of errors in
defining the problem or in formulating the linear
programming model.
3. Unboundedness
When the objective function
can
be
increased
(in
maximization problems) or
decreased (in minimization
problems) indefinitely without
violating any constraints, often
indicated by a line in the
feasible region that extends
infinitely in one direction.
4. Redundancy
When one constraint in a
linear programming problem is
essentially a duplicate of
another constraint, providing
no additional information to
FOUR SPECIAL
CASES IN
LINEAR
PROGRAMMING
An Unbounded Problem
the objective function is shown to
increase without bound; thus, a
solution is never reached.
Unlimited profits are not possible in
the real world; an unbounded solution,
like an infeasible solution, typically
reflects an error in defining the
problem or in formulating the model.
THANK YOU.
20XX
A COMPANY PRODUCES 2 BIKES, A MOUNTAIN BIKE
AND A ROAD BIKE. IT TAKES 3 HOURS TO ASSEMBLE
A MOUNTAIN BIKE AND 4 HOURS TO ASSEMBLE A
ROAD
BIKE.
THE
TOTAL
TIME
AVAILABLE
TO
ASSEMBLE IS 60 HOURS. THE COMPANY WANTS TO
HAVE TWICE AS MANY MOUNTAIN BIKES AS THE
ROAD BIKES. COMPANY MAKES A PROFIT OF $200
PER MOUNTAIN BIKE AND $100 PER ROAD BIKE. HOW
MANY ROAD BIKES AND MOUNTAIN BIKES TO
20XX