Deck 14: Solution concepts for linear programming

Question 1

Like the enumeration-of corner-points method,the simplex method evaluates all of the corner points of a problem

Answer 1

False

Question 2

In a linear programming problem with two decision variables,it is possible to have no point that satisfies all of the constraints simultaneously

Answer 2

True

Question 3

Most linear programming problems have just one optimal solution

Answer 3

True

Question 4

The optimal solution of a feasible linear programming problem includes at least one corner point of the feasible region

Question 5

The simplex method is an algorithm that can be used for solving only large-scale problems

Question 6

In a linear programming problem,there is always at least one optimal corner point

Question 7

If a linear programming problem does not have an optimal solution then it must be infeasible

Question 8

An optimal solution must lie on the boundary of the feasible region

Question 9

If the feasible region in a linear programming problem is unbounded,then the problem is unbounded

Question 10

The data given in Solver's sensitivity report are obtained directly from the output of the simplex method

Question 11

There are no feasible solutions to a problem when the constraints are too restrictive

Question 12

The simplex method can only solve problems with up to 100 functional constraints

Question 13

It is possible in some cases for a point inside the boundary of the feasible region to be an optimal solution

Question 14

A linear programming problem can have multiple optimal solutions

Question 15

The enumeration-of-corner-points method is limited because it can only solve problems with two decision variables

Question 16

If some necessary constraints were not included in a linear programming model,it is possible to have no limit on the best objective function value

Question 17

If a single optimal solution exists to a linear programming problem,it will exist at a corner point

Question 18

Problems with multiple optimal solutions always have at least two optimal corner points

Question 19

It can be helpful for management to have multiple optimal solutions

Question 20

It is possible to have more than one corner point of the feasible region as an optimal solution to a linear programming problem

Question 21

If a problem has more than one optimal solution then:

A)the slope of the objective function line is the same as one of the constraints
B)the problem was not formulated correctly
C)the problem must be re-solved
D)All of the above
E)None of the above

Question 22

Whenever possible,the initialization step of the simplex method chooses the origin to be the initial corner point

Question 23

In a linear programming problem,when the objective function is parallel to one of the constraints,then:

A)the solution is not optimal
B)multiple optimal solutions may exist
C)a single corner point optimal solution exists
D)no feasible solution exists
E)None of the above

Question 24

The simplex method chooses the adjacent corner point that is closest when searching for an optimal solution

Question 25

If a maximization problem has an objective function of 3x₁ + 10x₂,which of the following corner points is the optimal solution?

A)(0,2)
B)(0,3)
C)(3,3)
D)(5,1)
E)(0,0)

Question 26

The simplex method is a specific type of interior-point algorithm

Question 27

If a maximization problem has an objective function of 3x₁ + 2x₂,which of the following corner points is the optimal solution?

A)(0,2)
B)(0,3)
C)(3,3)
D)(5,1)
E)(0,0)

Question 28

If a problem is unbounded then:

A)the problem may not have been formulated correctly
B)the data may not have been entered correctly
C)at least one of the decision variable will have an optimal value of ∞
D)None of the above
E)All of the above

Question 29

For any linear programming problem,the best corner point must be an optimal solution

Question 30

The simplex method only considers adjacent corner points

Question 31

If a problem is infeasible,Solver will show the message "Set Cell values do not converge"

Question 32

Two corner points are adjacent to each other if they share all but one of the same constraint boundaries

Question 33

If a problem is infeasible then:

A)it was not formulated correctly
B)it is the constraints that are to blame,not the objective function
C)at least one of the decision variable will have an optimal value of infinity
D)None of the above
E)All of the above

Question 34

The theoretical limit on the number of decision variables that can be handled by the simplex method in a single problem is:

A)1
B)2
C)30
D)100
E)unlimited

Question 35

The computer time per iteration for an interior-point algorithm is approximately the same as for the simplex method

Question 36

Interior-point algorithms have limited capability for what-if analysis

Question 37

Management may choose a single product mix from among multiple optimal solutions because of:

A)a desire to highlight a new product
B)needs of an important customer
C)strategies adopted by competitors
D)All of the above
E)None of the above

Question 38

The simplex method is the standard procedure for solving linear programming problems with any number of decision problems because:

A)it is an efficient procedure
B)spreadsheets are not always available
C)it provides the information necessary for what-if analysis
D)a and b only
E)a and c only

Question 39

A linear programming problem may have:

A)II and IV only
B)II and III only
C)I,II,and III only
D)I,II,and IV only
E)All of the above

Question 40

Management science algorithms are typically iterative algorithms

Question 41

Interior-point algorithms:

A)are far more complicated than the simplex method
B)require more computation time per iteration that the simplex method
C)tend to be much faster than the simplex method for huge problems
D)All of the above
E)a and b only

Question 42

The simplex method includes which of the following components?

A)An initialization step
B)An optimality test
C)A trial step
D)All of the above
E)a and b only

Question 43

The simplex method is which kind of algorithm?

A)iterative
B)repetitive
C)systematic
D)All of the above
E)None of the above

Question 44

The ability to solve large problems with the simplex method is limited primarily by:

A)the number of decision variables
B)the size of the parameters in the model
C)the number of functional constraints
D)the software package chosen
E)None of the above

Question 45

When choosing which corner point to advance to next,the simplex method chooses the one:

A)that is closest
B)along the edge with the largest rate of improvement
C)along the edge with a negative rate of improvement
D)that is furthest from the origin
E)None of the above