Deck 8: Nonlinear Programming

Question 1

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

Answer 1

True

Question 2

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

Answer 2

True

Question 3

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

Answer 3

False

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

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

Question 10

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

Question 11

Applying separable programming requires having profit graphs that are smooth curves.

Question 12

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

Question 13

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.

Question 14

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

Question 15

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

Question 16

A nonlinear function may contain a product of two variables.

Question 17

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

Question 18

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 19

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

Question 20

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

Question 21

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 22

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

Question 23

A linear function may contain which of the following?

A)A term that contains a single variable with an exponent of 1.
B)A term that contains a single variable with an exponent of 2.
C)A term that is a constant times the product of two variables.
D)All of the above.
E)b.and c.only.

Question 24

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

Question 25

Solver Table can be used for nonlinear programming problems to systematically try a number of different starting points.

Question 26

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

Question 27

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

Question 28

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

Question 29

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 30

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 31

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 32

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

Question 33

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

Question 34

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 35

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

Question 36

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

Question 37

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

Question 38

Two runs of the Evolutionary Solver on the same problem will typically yield the same solution.
Multiple Choice Questions

Question 39

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

Question 40

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

Question 41

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 Solver Table to try different starting points.
C)Using Evolutionary Solver.
D)All of the above.
E)b and c only.

Question 42

Which of the following are disadvantages of the Evolutionary Solver?

A)It does not deal well with complicated objective functions.
B)It does perform well on models with many constraints.
C)It is easily trapped at local optima.
D)a and b.
E)None of the above.

Question 43

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 44

A nonlinear function may contain which of the following?

A)A term that contains a single variable with an exponent of 1.
B)A term that contains a single variable with an exponent of 2.
C)A term that is a constant times the product of two variables.
D)All of the above.
E)b.and c.only.

Question 45

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 46

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 47

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 48

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 49

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 50

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 51

A nonlinear programming problem may have:

A)activities with increasing marginal returns.
B)activities with decreasing marginal returns.
C)nonlinear functional constraints.
D)All of the above.
E)b.and c.only.

Question 52

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 53

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

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