Problem 8-7
Part c – How much may the objective function coefficients (i.e., c1 and c2) change
without changing the optimal solution? How much may the right hand side values of
the constraint equations (i.e., q1 and q2) change without changing the optimal
solution?\
Let X1 be the number of half page ads in the Sunday Chicago Tribune news paper
and let X2 be the number of television spots.
The objective is to minimize the advertising cost. The objective function is
Z = 925 X1 + 2,000 X2.
The minimum exposure level within the city’s neighborhood is 40%. This leads to
the constraint
4 X1 + 5X2 ≥ 40.
The minimum exposure level in the northwest suburbs is 60%. This leads to the
constraint
3 X1 + 3X2 ≥ 60.
Also the variables X1, X2 are to be nonnegative integers.
So the LPP can be formulated as
Minimize Z = 925 X1 + 2,000 X2
Subject to
4 X1 + 5X2 ≥ 40
3 X1 + 3X2 ≥ 60
X1 ≥ 0
X2≥ 0
X1 is integer
X2 is integer.
Computer output
Data
X1
Objective
Constraint 1
Constraint 2
Results
Variables
Objective
X2
925
4
3
2000
5
3
20
0
>
>
0
40
60
18500
Results
LHS
18500
80
60
Slack/Surplus
-40
0
Sensitivity analysis
The value of c1=925 can be taken as any value ≤ 2000 without changing the
optimum solution, other things remaining the same.
The value of c2=2000 can be taken as any value ≥ 925 without changing the
optimum solution, other things remaining the same.
The value of b1=40 can be taken as any value ≤ 80 without changing the optimum
solution, other things remaining the same.
The value of b2=60 can be taken as any value ≤60 without changing the optimum
solution, other things remaining the same.