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The study of how changes in the coefficients of a linear program-
ming problem affect the optimal solution.
Range of optimality
The range of values over which an objective function coefficient
may vary without causing any change in the values of the decision variables in the opti-
mal solution.
Dual price
The improvement in the value of the objective function per unit increase in
the right-hand side of a constraint.
Reduced cost
The amount by which an objective function coefficient would have to im-
prove (increase for a maximization problem, decrease for a minimization problem) before
it would be possible for the corresponding variable to assume a positive value in the opti-
mal solution.
Range of feasibility
The range of values over which the dual price is applicable.
100 percent rule A
rule indicating when simultaneous changes in two or more objective
function coefficients will not cause a change in the optimal solution. It can also be applied
to indicate when two or more right-hand-side changes will not cause a change in any of the
dual prices.
Sunk cost A
cost that is not affected by the decision made. It will be incurred no matter
what values the decision variables assume.
Relevant cost A
cost that depends upon the decision made. The amount of a relevant cost
will vary depending on the values of the decision variables.
PROBLEMS
SELFm
1. Consider the following linear program:
Max
3A
+
2B

Chapter 3
Linear Programming: Sensitivity
Analysis
and Interpretation of Solution
a.
Use the graphical solution procedure to find the optimal solution.
b.
Assume that the objective function coefficient for A changes from
3
to
5.
Does the
optimal solution change? Use the graphical solution procedure to find the new opti-
mal solution.
c.
Assume that the objective function coefficient forA remains
3,
but the objective func-
tion coefficient for B changes from 2 to
4.
Does the optimal solution change? Use the
graphical solution procedure to find the new optimal solution.
d.
The Management Scientist computer solution for the linear program in part (a) pro-
vides the following objective coefficient range information:
Variable
Lower
Lit
Current Value
Upper
A
2
3
6
Use this objective coefficient range information to answer parts (b) and (c).
2.
Consider the linear program in Problem
1.
The value of the optimal solution is 27. Sup
pose that the right-hand side for constraint
1
is increased from
10
11.
a.
Use the graphical solution procedure to find the new optimal solution.
Use
the solution to part (a) to determine the dual price for constraint
1.
The Management Scientist computer solution for the linear program in Problem
1
pro-
vides the following right-hand-side range information:
Lower
Limit
Current Value
Upper
8
10
11.2
2
18
24
30
3
13
16
No Upper Limit
What does the right-hand-side range information for constraint
1
tell you about the
dual price for constraint l?

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