SUPPLEMENT TO CHAPTER 6:
LINEAR PROGRAMMING
Teaching Notes
The main goal of this supplement is to provide the students with an overview of the types of problems
that have been solved using linear programming (LP). In the process of learning the different types of
problems that can be solved with LP, the students must also develop a very basic understanding of the
assumptions and special features of LP problems.
The students should also learn the basics of developing and formulating linear programming models for
simple problems, solve twovariable linear programming problems by the graphical procedure and
interpret the resulting outcome. In the process of solving these graphical problems, we must stress the role
and importance of extreme points in obtaining an optimal solution.
The improvements in computer hardware and software technology and popularity of the software package
Microsoft Excel makes the use of computers in solving linear programming problems accessible to many
users. Therefore, a main goal of the chapter should be to allow students to solve linear programming
problems using Excel.
More importantly, we need to make sure that the students are able to interpret the
results obtained from Excel or any another computer software package.
Answers to Discussion and Review Questions
1.
Linear programming is wellsuited to an environment of certainty.
2.
The “area of feasibility,” or
feasible solution space
is the set of all combinations
of values of the decision variables which satisfy the constraints. Hence, this area is
determined by the constraints.
3.
Redundant constraints do not affect the feasible region for a linear programming
problem.
Therefore, they can be dropped from a linear programming problem without
affecting the optimal solution.
4.
An isocost line represents the set of all possible combinations of two inputs that
will result in a given cost. Likewise, an isoprofit line represents all of the possible
combinations of two outputs which will yield a given profit.
5.
Sliding an objective function line towards the origin represents a decrease in its
value (i.e., lower cost, profit, etc.). Sliding an objective function line away from the origin
represents an
increase
in its value.
6.
a.
Basic variable
: In a linear programming solution, it is a variable
not required to equal zero.
b.
Shadow price
: It is the change in the value of the objective function per unit
increase in a constraint right hand side.
c.
Range of feasibility
: The range of values over which a constraint’s right hand
side value may vary without changing the optimal basic feasible solution.
d.
Range of optimality
: The range of values over which a variable’s objective
function value may vary without changing the current optimal basic feasible solution.
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 Spring '11
 fsafas
 Linear Programming, Optimization, objective function, X1

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