QMB 3602 Chapter 8 Nonlinear Programming
Which of the following profit functions could be the objective function in a quadratic programming problem? 3x - y^2 x^2 + 2x - 3 x^3 + 3x -4
3x - y^2
A firm has graphed its profits versus the advertising expenditure. The graph has one peak at an advertising level of $10,000 (profits equal to $25,000) and another peak at an advertising level of $25,000 (when profits equal $20,000). Which of the following is true (select all that apply) An advertising level of $10,000 is the global maximum An advertising level of $25,000 is the global maximum An advertising level of $25,000 is the local maxima An advertising level of $10,000 is the local maxima
An advertising level of $10,000 is the global maximum An advertising level of $25,000 is the local maxima An advertising level of $10,000 is the local maxima
In Analytic Solver, the user can identify which element of the model violate the assumptions of linearity by using the ____________ ____________ Model tool
Analyze Original
If the costs of an activity increases at a faster and faster rate as the activity level increases, which of the following could be used to represent these costs if x is the level of the activity?
Costs = x^2
If Analytic Solver's "Automatically Select Engine" option is turned on, Analytic Solver will use __________ Solver if the model's objective function has discontinuities.
Evolutionary
Which of the following statements about Evolutionary Solver are TRUE? (select all that apply) Evolutionary Solver can evaluate complex objective functions better than Nonlinear Solver Nonlinear Solver is less likely than Evolutionary Solver to be unable to overcome discontinuities Evolutionary Solver is less likely than Nonlinear Solver to be unable to overcome discontinuities Nonlinear Solver can evaluate complex objective functions better than Evolutionary Solver
Evolutionary Solver can evaluate complex objective functions better than Nonlinear Solver Evolutionary Solver is less likely than Nonlinear Solver to be unable to overcome discontinuities
Which of the following statements about Evolutionary Solver are FALSE? (select all that apply) Evolutionary Solver uses a random search process to identify solutions Evolutionary Solver is guaranteed to identify the optimal solution in a reasonable amount of time Evolutionary Solver is generally faster than Nonlinear Solver
Evolutionary Solver is guaranteed to identify the optimal solution in a reasonable amount of time Evolutionary Solver is generally faster than Nonlinear Solver
T/F: A function that is piecewise linear can have discontinuities
False
T/F: Solving a nonlinear programming problem using the Multistart approach is guaranteed to identify the globally optimal solution
False
In Solver, nonlinear models require use of which solution method?
GRG Nonlinear
When an activity has increasing marginal returns, which of the following statements is TRUE (select all that apply) Incremental costs do not increase as the level of the activity increases Incremental costs may increase as the level of the activity increases Incremental costs may decrease as the level of the activity increases
Incremental costs do not increase as the level of the activity increases Incremental costs may decrease as the level of the activity increases
When an activity has increasing marginal returns, which of the following statements is TRUE? (select all that apply) Incremental costs do not increase as the level of the activity increases Incremental costs may decrease as the level of the activity increases Incremental costs may increase as the level of the activity increases
Incremental costs do not increase as the level of the activity increases Incremental costs may decrease as the level of the activity increases
When an activity has increasing marginal returns, which of the following statements is FALSE? (select all that apply) Incremental profits do not increase as the level of the activity increases Incremental profits may decrease as the level of the activity increases Incremental profits may increase as the level of the activity increases
Incremental profits do not increase as the level of the activity increases Incremental profits may decrease as the level of the activity increases
Which of the following can cause nonlinearity in a model? (select all that apply) Use of linear operators such as addition Interactions between decision variables Use of nonlinear operators such as square roots
Interactions between decision variables Use of nonlinear operators such as square roots
Separable programming is very valuable because Fewer decision variables are needed in a separable programming model All nonlinear problems can be addressed using separable programming It allows a nonlinear problem to be solved using linear programming techniques
It allows a nonlinear problem to be solved using linear programming techniques
Which of the following is an advantage of using a linear approximation of a nonlinear function? (select all that apply) The model is more precise Linear models can be solved easier Linear models are easier to formulate
Linear models can be solved easier Linear models are easier to formulate
Nonlinear Solver can only identify a single local _________, which may not be the global _________
Maxima: Maximum
Which of the following types of nonlinear models are often difficult to solve? (select all that apply) Models that are piecewise linear Models with increasing marginal returns Models with discontinuities
Models with increasing marginal returns Models with discontinuities
The __________ feature of Solver addresses the problem of multiple local optima in nonlinear programming by solving the problem multiple times, each with a different starting point
Multistart
Which of the following are operations that the user can choose in Evolutionary Solver (select all that apply) Mutation size Mutation rate Population size
Mutation rate Population size
_____ models are used when the relationship between activity levels and the overall measure of performance is nonproportional
Nonlinear
If a graph consists of a sequence of connected line segments, it is ______________ ______________
Piecewise Linear
If a nonlinear profit function can be divided into separate line segments where the proportionality and linearity assumptions are not violated, the __________ programming technique can be used to find a solution
Separable
_______ programming can be used when a problem with decreasing marginal returns is also piecewise linear
Separable
The problem of multiple local optima in nonlinear programming can be addressed by
Solving the problem multiple times, each with a different starting point
If a model has only one output cell which is nonlinear
The entire model is nonlinear
Which of the following is an advantage of using a nonlinear programming model? The nonlinear model is easier to solve than a linear model The nonlinear model is easier to formulate than a linear model The model is a better representation of reality than a linear approximation
The model is a better representation of reality than a linear approximation
Which of the following statements about quadratic programming problems is TRUE? (select all that apply) The objective function is piecewise linear The objective function has a quadratic form The problem has decreasing marginal returns
The objective function has a quadratic form The problem has decreasing marginal returns
T/F: Analytic solver can be used to analyze a model to identify the most appropriate method of solving
True
In Analytic Solver, the user can identify which elements of the model violate the assumptions of linearity by
Using the Analyze Original Model tool
For a minimization problem, Nonlinear Solver will always identify a local minima the global minimum all local minima points
a local minima
If a nonlinear programming problem requires that no two decision variables have the same value, the _______________ constraint can be used to enforce this requirement
alldifferent
If data can be graphed in an X-Y scatter plot, the nonlinear relationship between X and Y can be identified by using which tool in Excel? equation editor curve fitting method formula builder
curve fitting method
For a nonlinear model with _________ marginal returns, Nonlinear Solver will always identify the globally optimal solution
decreasing
When the incremental profit associated with an increase in the level of an activity never increases and may decrease, the activity is said to have ____________ marginal returns.
decreasing
If a graph of a function consists of line segments that are not connected, the gaps between line segments are known as line spaces discontinuities thresholds
discontinuities
A _______________ algorithm uses ideas from biology to find solutions to nonlinear problems
genetic
The major advantage of using nonlinear programming is the _________ in seeking the best solution for the real problem lesser time taken lesser cost involved greater precision it provides greater reliability it provides
greater precision it provides
Separable programming can not be applied to problems when the activities have _____________ marginal returns
increasing
When the incremental profit associated with an increase in the level of an activity never decreases and may increase, the activity is said to have _______________ marginal returns
increasing
The objective function in a nonlinear programming model
is often a combination of linear and nonlinear terms
If all relationships in a model are proportional, the model is ____________
linear
Separable programming is used to convert a nonlinear problem with decreasing marginal returns which is also a piecewise linear into a __________ programming problem
linear
When the graph of a function has discontinuities, the function is linear nonlinear piecewise linear
nonlinear
In genetic algorithm =, the set of candidate solutions is called the
population
If a nonlinear problem has the objective function "Profit = 15x - x^2", where x is the number of units sold, the problem can be solved using _____________ programming
quadratic
Linear formulas can use which of the following arithmetic operations? (select all that apply) exponents subtraction multiplication addition
subtraction multiplication addition
