Chapter 3

Question 1

Sensitivity Analysis

Answer 1

study of how changes in coefficients of optimization model (min or max) affect optimal solution

Question 2

What do we want to determine with sensitivity analysis?

Answer 2

How much these changes will affect optimal solution of LPM

Question 3

Two questions answered with sensitivity analysis

Answer 3

how will change in coefficient of objective function affect optimal solution?
how will change in right side value of constraint affect optimal solution

Question 4

Feasible solution satisfies all….

Answer 4

solution that satisfies all constraints

Question 5

feasible set or region

Answer 5

set of all feasible solutions

Question 6

Optimal solution

Answer 6

feasible solution that produces the best objective function of all feasible solutions

Question 7

When does sensitivity analysis begin

Answer 7

after original optimal solution of LP model is estalished

Question 8

sensitivity analysis is also known as

Answer 8

post-optimality analysis

Question 9

Binding constraints

Answer 9

constraints satisfied exactly at optimal solution, S=0

Question 10

Binding constraints are constraints whose intersection…….

Answer 10

determines optimal solution to LP Model

Question 11

Non binding constraints

Answer 11

constraints that are satisfied at the optimal solution but have surplus -S and slack +S whose value is not zero

Question 12

Range of optimality

Answer 12

range of values for each variable of objection function coefficient which current solution will remain optimal

Question 13

Range of optimality changes to variables at a time

Answer 13

only one variable coefficient change at a time

Question 14

Does increase or decrease of a objection function coefficient change the values of decision variables in optimal solution

Answer 14

no they cannot if in optimal range

Question 15

what if coefficient change for objection function is outside range

Answer 15

Manage will have to resolve linear program model, change should not be allowed, would result in new optimal solution, cannot guarantee optimality for other variables

Question 16

Shadow price

Answer 16

amount by which optimal objection value will change if right hand side of constraint is increase or decreased by one unit

Question 17

Other terms for Shadow Price

Answer 17

marginal value or dual price

Question 18

Shadow price is equal to

Answer 18

different in values of objective function between new and original problem

Question 19

Shadow price for non-binding constraint is….

Answer 19

zero

Question 20

negative shadow price indicates

Answer 20

objective function will not improve if RHS is increased

Question 21

Range of Feasibility

Answer 21

range of values over which a right hand side value may vary without changing the value and interpretation of shadow price

Question 22

Any change to right hand side of binding constraint will……

Answer 22

change the optimal solution

Question 23

Any change to right hand side of non-binding constraint that is less than slack or surplus will……

Answer 23

will cause no change to optimal solution as S is zero

Question 24

Reduced Cost

Answer 24

minimum amount by which objective coefficient of a variable should change in order to affect optimal solution

Question 25

Case Maximization: If reduced cost is < 0

Answer 25

cost of consumed is higher than profit, activity should not be undertaken

Question 25

Case maximization: Reduced cost =

Answer 25

per unit profit of activity - cost of consumed resource per activity
* per unit of resource is priced at shadow price

Question 26

Case Maximization: if reduced cost >= 0

Answer 26

cost of consumed is lower/equal to profit, activity is economically attractive

Question 27

Case minimization: Reduced cost =

Answer 27

per unit cost of activity - cost of consumed resource per activity
* per unit of resource is priced at shadow price

Question 28

Case Minimization: If reduced cost is > 0

Answer 28

cost of consumed is higher than cost of activity so it should not be undertaken

Question 29

Case Minimization: If reduced cost is <= 0

Answer 29

cost of consumed is lower than or equal to cost of activity is economically attractive

Question 30

Variable value increase indication of worse objective value.
- Maximization
- Minimization

Answer 30

Maximization: R is negative and objective decrease
Minimization: R is Positive and objective increase