MODELING WITH LINEAR
PROGRAMMING
CHAPTER 2
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◦ A Linear Programming model seeks to maximize or minimize a linear
function, subject to a set of linear constraints.
◦ The linear model consists of the following
components:
◦ A set of decision variables that we seek to determine.
◦ An objective function that we need to optimize(maximize or minimize).
◦ A set of constraints that the solution must satisfy.
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Two variable LP Problem
First we discuss the graphical solution of a twovariable LP.
Though two-variable problems hardly exist in
practice, the treatment provides concrete
foundations for the development of the general
simplex algorithm
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Example
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Some constraints
◦ The daily demand for interior paint cannot exceed that for
exterior paint by more than 1 ton.
◦ Also, the maximum daily demand for interior paint is 2 tons.
Reddy Mikks wants to determine the
optimum (best) product mix of interior
and exterior paints that maximizes the
total daily profit
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The Graphical Analysis of Linear
Programming
The set of all points that satisfy all the
constraints of the model is called a
FEASIBLE REGION
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The feasible solution space is ABCDEF
in which all the constraints are
satisfied (verify!).
All points outside the boundary of the
area ABCDEF are infeasible.
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