Deck 8: Non linear programming

Question 1

In problems where the objective is to minimize the total cost of the activities,an activity is said to have decreasing marginal returns if the slope of its cost graph never increases but sometimes decreases as the level of the activity increases

Answer 1

False

Question 2

A quadratic programming problem is a special type of linear programming problem

Answer 2

False

Question 3

In separable programming,if an activity violates the proportionality assumption it must have increasing marginal returns

Answer 3

False

Question 4

Having activities with decreasing marginal returns is the only way that the proportionality assumption can be violated

Question 5

Nonlinear programming problems with decreasing marginal returns are generally easier to solve then nonlinear programming problems with increasing marginal returns

Question 6

In separable programming,each activity that violates the proportionality assumption is separated into parts with a new variable for each part

Question 7

A nonlinear function may contain a product of two variables

Question 8

Separable programming is applicable when there are increasing or decreasing marginal returns

Question 9

In some cases of separable programming,the profit graphs will be curves rather than a series of line segments

Question 10

Sometimes the Solver can return different solutions when optimizing a nonlinear programming problem

Question 11

If C1 is a changing cell,then ROUND(C1)is a linear function

Question 12

A local maximum is always a global maximum in a nonlinear programming problem

Question 13

When the marginal return from an activity decreases on a continuous basis,the profit graphs will consist of a series of line segments

Question 14

If the slope of a graph never increases but sometimes decreases as the level of the activity increases,then it is said to have decreasing marginal returns

Question 15

Linear programming assumes that the profit from each activity is proportional to the level of that activity

Question 16

If D1 is a data cell,and C1 and C2 are changing cells,then IF(D1 >= 2,C1,C2)is a linear function

Question 17

If C1:C6 are all changing cells,then SUMPRODUCT(C1:C3,C4:C6)is a linear function

Question 18

Applying separable programming requires having profit graphs that are smooth curves

Question 19

Excel's curve fitting method is used to find the values of the parameters for an equation that best fit data

Question 20

Excel's curve fitting method is used to graph a nonlinear equation

Question 21

Two runs of the Evolutionary Solver on the same problem will typically yield the same solution

Question 22

When applying nonlinear programming to portfolio selection,a trade-off is being made between the expected return and the risk associated with the investment

Question 23

If the RSPE Model Analysis indicates that the model is NLP Convex,then only the Evolutionary Solver can be counted on to yield near optimal solutions

Question 24

Evolutionary Solver is often faster than the standard Solver at solving linear programming problems

Question 25

Mutation is the technique used to create the next generation of solutions in the Evolutionary Solver

Question 26

The members of the population used to create the next generation are picked randomly by the Evolutionary Solver

Question 27

If the data cells are in column D and the changing cells are in column C,which of the following are not linear formulas in a spreadsheet?

A)IF(D1 >= 6,C1,C2)
B)ROUND(C3)
C)ABS(C3)
D)All of the above
E)b and c only

Question 28

If the RSPE Model Analysis indicates that the model is a NSP,then the GRG Nonlinear search method is the best one to use

Question 29

The additivity assumption of linear programming states that each term in the objective function is the sum of two or more variables

Question 30

The risk for a portfolio is decreased when the particular stocks tend to move up and down together

Question 31

Profit = 3x₁ + 2x₂ + 9x₁x₂ is an example of a nonlinear function

Question 32

Evolutionary Solver uses an algorithm based on genetics,evolution,and survival of the fittest

Question 33

The multistart feature in Solver can be used for nonlinear programming problems to systematically try a number of different starting points

Question 34

When there are decreasing marginal returns:

A)the slope of the graph never increases but sometimes decreases
B)the slope of the graph never decreases but sometimes increases
C)the graph always consists of a smooth curve
D)the graph always consists of a series of line segments
E)separable programming should not be used

Question 35

Trying different starting points and picking the best solution will always yield the optimal solution to a nonlinear programming problem

Question 36

Sometimes Evolutionary Solver will make a random change in a member of the population

Question 37

It now is common practice for professional managers of large stock portfolios to use computer models based partially on separable programming

Question 38

The Nonlinear Solver keeps track of a large set of candidate solutions,called the population

Question 39

If the data cells are in column D and the changing cells are in column C,which of the following are linear formulas in a spreadsheet?

A)SUMPRODUCT(D1:D6,C1:C6)
B)SUMPRODUCT(C1:C3,C4:C6)
C)SUM(C1:C6)
D)All of the above
E)a and c only

Question 40

The additivity assumption can be violated by nonlinear programming because of cross-product terms involving the product of two variables

Question 41

Separable programming will always find the optimal solution when the following is true:

A)The profit or cost graph is piecewise linear
B)There are decreasing marginal returns
C)a and b must both be true
D)Separable programming only finds an approximate solution
E)None of the above

Question 42

The measure of risk for pairs of stocks in a portfolio selection problem is called:

A)the covariance of the return
B)the variance of the return
C)the expected return
D)decreasing marginal return
E)None of the above

Question 43

Which of the following can be part of a nonlinear profit graph?

A)Decreasing marginal returns
B)Increasing marginal returns
C)Discontinuities
D)All of the above
E)a and b only

Question 44

Which of the following techniques is appropriate when a nonlinear programming problem has multiple local optima?

A)Running Solver many times with different starting points
B)Using the multistart feature to try different starting points
C)Using Evolutionary Solver
D)All of the above
E)b and c only

Question 45

Decreasing marginal returns violates which assumption of linear programming?

A)The proportionality assumption
B)The divisibility assumption
C)The additivity assumption
D)All of the above
E)None of the above

Question 46

Which of the following are advantages of the Evolutionary Solver?

A)The complexity of the objective function does not matter
B)It will always find the optimal solution
C)It is faster than the standard Solver
D)It always finds the same solution
E)None of the above

Question 47

If a model uses IF or ROUND functions that incorporate the changing cells,then running the RSPE Analyze Model without Solving feature will typically say the model is of what type?

A)Linear
B)NLP Convex
C)QP Convex
D)NSP
E)None of the above

Question 48

Evolutionary Solver is best suited to which kinds of problems?

A)Linear programs
B)Nonlinear programs with difficult objective functions
C)Nonlinear programs with decreasing marginal returns and no discontinuities
D)Nonlinear programs with many constraints
E)None of the above

Question 49

Evolutionary Solver is based on which of the following concepts?

A)Genetics
B)Evolution
C)Survival of the Fittest
D)All of the above
E)b and c only

Question 50

The requirement that each term in the objective function only contains a single variable is in a linear program is referred to as:

A)the proportionality assumption
B)the divisibility assumption
C)the additivity assumption
D)a nonlinear function
E)None of the above

Question 51

The measure of risk in a portfolio selection problem is called:

A)the covariance of the return
B)the variance of the return
C)the expected return
D)decreasing marginal return
E)None of the above

Question 52

Which of the following is an example of a nonlinear function?

A)Profit = 5x?₁ + 7x₂ ?- 2x₂²
B)Profit = 8x₁x₂ - x₁² - 4x₂²
C)Profit = x₁ + 6x₂ + 3x₁x₂
D)None of the above
E)All of the above