ISEN 320
Operations Research I
Fall
2023
In-class Exercise
Consider the following LP
max
z
=
3
x
1
+
6
x
2
+
20
x
3
s
.
t
.
-
2
x
1
+
8
x
2
+
5
x
3
≤
40
2
x
1
-
4
x
2
+
3
x
3
≤
12
-
4
x
1
+
6
x
2
+
4
x
3
≤
36
x
1
, x
2
, x
3
≥
0
Using AMPL, solve the LP and answer the following questions.
1. What is the optimal solution for the LP?
2. What is the reduced cost for each decision variable?
3. What range of values can the objective function coefficient of
x
1
take without
impacting the optimality of the current basis?
4. What range of values can the objective function coefficient of
x
2
take without
impacting the optimality of the current basis?
5. What range of values can the objective function coefficient of
x
3
take without
impacting the optimality of the current basis?
6. What range of values can the right hand side of the first constraint take without
impacting the optimality of the current basis?
7. What range of values can the right hand side of the second constraint take without
impacting the optimality of the current basis?
8. What range of values can the right hand side of the third constraint take without
impacting the optimality of the current basis?
9. What is the optimal dual solution? How much would a company be willing to pay
for each of the three resources.
10. Using the dual solution and the sensitivity analysis conducted, what would the new
optimal objective function value be if the right hand side of the first constraint is
reduced from 40 to 20? Explain your reasoning.
