# Quiz 13: Nonlinear Models:dynamic, Goal, and Nonlinear Programming

Business

Q 1Q 1

Sootaway Chimney Cleaners has a preemptive goal programming model for their three goals: reduce cost, reduce personnel, and raise quality.If goal 2 has a higher priority than goal 3, it is not possible for goal 3 to be met unless goal 2 has been met first.

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True False

False

Q 2Q 2

One solution approach for solving a dynamic programming model is a backwards recursion approach.

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True False

True

Q 3Q 3

Simply put, Bellman's principle of optimality states that the
optimal path to the end of the process does not depend upon how the
current state was reached.

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True False

True

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True False

Q 5Q 5

A goal programming problem can be transformed into a series of linear programming problems, each of which has a different objective function and one more constraint than the previous one in the series.

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True False

Q 6Q 6

In a convex programming problem, while the objective function can have any shape, the set of constraints must form a convex set.

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True False

Q 7Q 7

In a mathematical model with two variables, a function which is both concave and convex is a straight line.

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True False

Q 8Q 8

For a convex nonlinear programming problem, the Kuhn-Tucker
conditions are both necessary and sufficient.

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True False

Q 9Q 9

LaGrange multipliers are like shadow prices in that they give the "instantaneous" change to the objective function value for changes to right hand side coefficients.

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True False

Q 10Q 10

While the optimal solution to a constrained nonlinear model need not occur at an extreme point, it must occur at a boundary point.

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True False

Q 11Q 11

According to goal programming proponents, most business problems have conflicting objectives and cannot be solved by optimizing a linear programming model with a single objective function.

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True False

Q 12Q 12

Efficient solution procedures, guaranteed to provide optimal solutions, exist for convex programming and quadratic programming.

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True False

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True False

Q 14Q 14

In a dynamic program, the boundary conditions refer to the first stage, and the stopping rule refers to the last stage.

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True False

Q 15Q 15

The optimal solution for an unconstrained concave function occurs where the slope equals zero for all variables.

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True False

Q 16Q 16

Quadratic programming is a special case of __________ programming.
A)standard linear
B)general nonlinear
C)goal
D)dynamic

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Multiple Choice

Q 17Q 17

In applying Bellman's principle of optimality for dynamic programming using backwards recursion for a maximization problem, at a given state within a given stage:
A)it does not matter how that state is reached.
B)that state was reached using an optimal set of decisions from the first stage.
C)the shortest distance route to the next stage will be selected.
D)the longest distance route to the next stage will be selected.

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Multiple Choice

Q 18Q 18

Which of the following may be said to have no single form?
A)Standard linear programming.
B)Integer linear programming.
C)Binary linear programming.
D)Dynamic programming.

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Multiple Choice

Q 19Q 19

Variables raised to a power other than 1, may be found in a nonlinear programming problem.Other nonlinearities include:
A)cross products, but not quotients.
B)quotients, but not cross products.
C)either cross products or quotients.
D)neither cross products nor quotients.

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Multiple Choice

Q 20Q 20

Dynamic programming is so named because:
A)optimal solutions derived change over time.
B)it deals with multistage scenarios.
C)its parameters are not constant.
D)it allows for a range of decisions.

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Multiple Choice

Q 21Q 21

Stages in a dynamic programming problem might represent any of the following except:
A)system states.
B)time, in months.
C)projects.
D)"knapsack" items.

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Multiple Choice

Q 22Q 22

The fundamental approach to solving dynamic programming problems may be characterized as:
A)forward incursion.
B)backwards recursion.
C)total enumeration.
D)networking.

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Multiple Choice

Q 23Q 23

The "knapsack problem" may be solved using a __________ programming technique.
A)dynamic
B)goal
C)quadratic
D)binary

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Multiple Choice

Q 24Q 24

Which of the following need not be part of a dynamic programming model?
A)Linear constraints.
B)Boundary conditions.
C)A return function for each possible decision at each stage.
D)An optimal value function.

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Multiple Choice

Q 25Q 25

In goal programming, the multiple objectives (goals) must be:
A)complementary.
B)conflicting.
C)preemptive.
D)prioritized.

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Multiple Choice

Q 26Q 26

Which of the following is true about the optimal solution to a general nonlinear model?
A)All partial derivatives of the objective function must equal 0.
B)It must occur at a boundary point.
C)All nonlinear constraints must be satisfied.
D)The LaGrange multipliers must all be 0.

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Multiple Choice

Q 27Q 27

In goal programming, the weights assigned to deviations from goals:
A)must sum to 1.
B)may not be equal.
C)may be negative.
D)must all be nonnegative.

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Multiple Choice

Q 28Q 28

In goal programming, deviation variables, E

_{1}and U_{1}: A)may appear in the objective function and several constraints. B)will appear in the objective function and exactly one constraint. C)must both be 0 in the optimal solution. D)can both be positive in the optimal solution.Free

Multiple Choice

Q 29Q 29

In a goal programming model in which goal 1 has a higher priority than goal 2:
A)if goal 1 is not met, goal 2 will not be met.
B)if goal 2 is met, goal 1 will be met.
C)goal 2 may be met even if goal 1 is not.
D)goal 1 and goal 2 cannot both be met.

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Multiple Choice

Q 30Q 30

For general nonlinear programming problems, the Kuhn-Tucker conditions:
A)will not be satisfied by a non-optimal solution.
B)must be satisfied by an optimal solution.
C)are satisfied only at boundary points.
D)are satisfied at extreme points and may be satisfied at boundary points.

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Multiple Choice

Q 31Q 31

LaGrange multipliers are:
A)partial derivatives.
B)nonzero only for an optimal solution.
C)shadow prices.
D)used to verify feasibility.

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Multiple Choice

Q 32Q 32

The optimal solution to a constrained nonlinear programming problem __________ occur at a boundary point.
A)must
B)cannot
C)need not
D)should not

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Multiple Choice

Q 33Q 33

How can we investigate minor changes to the parameters of a dynamic programming problem?
A)Sensitivity analysis.
B)Trial and error.
C)Kuhn-Tucker equations.
D)Review the output from the intermediate stages.

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Multiple Choice

Q 34Q 34

The objective of goal programming is a solution that:
A)meets the highest priority goal and satisfies all constraints.
B)satisfies all constraints and comes closest to meeting the goals.
C)meets the goals and minimizes constraint violation.
D)satisfies constraints as modified by the detrimental deviations.

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Multiple Choice

Q 35Q 35

Which of the following is not a true description of concave functions?
A)No sharp points or discontinuities.
B)A single peak.
C)A line between two points on the curve will lie on or below the curve.
D)Nonlinear.

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Multiple Choice

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Q 38Q 38

Under what conditions would you choose to use a standard linear programming technique for a nonlinear programming problem?

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Q 39Q 39

Briefly describe the concept of backwards recursion in the dynamic programming solution approach.

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Q 40Q 40

If, in a nonlinear programming model classified as convex, the
goal is to maximize a concave objective function, why is it referred to as a convex problem? What would happen if the objective function were convex?

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Q 41Q 41

Can a dynamic programming approach be used to solve a production/inventory problem possessing an infinite planning horizon?

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Q 42Q 42

Without writing equations, what are the basic components to the Kuhn-Tucker conditions for a maximization problem with "≤" constraints?

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Q 43Q 43

How does the number of computations for a dynamic programming model compare to total enumeration?

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Q 46Q 46

A college student has five full days until his next, and last, final exam.While he feels the need to study heavily for the test, he also needs to put in time on his job to pay living expenses.

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Q 47Q 47

Terrestrial Telescope manufactures the Orion telescope at its Ohio plant.It has been determined that the number of telescopes it can make weekly is a function of the amount of its $20,000 weekly budget allocated to salaries, X

_{1}, and to equipment, X_{2}.When X_{1}and X_{2}are expressed in $1,000's, an economic study has shown that the number of telescopes produced can be expressed as the concave functionFree

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Q 49Q 49

For the problem faced by Kelso Construction in problem 4, how should the crews be allocated?

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Q 50Q 50

As part of its Welfare to Work program, the Georgia legislature has allocated $28,800,000 to a new program designed to get skilled and unskilled workers off welfare.Unskilled workers would be paid $7.20 per hour whereas skilled workers would be paid $12.00 per hour under this program.The goals of the program are: (1) to generate at least 2,000,000 man-hours of work;

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Q 51Q 51

Consider the Welfare to Work program in problem 8.Suppose now that a nonpreemptive approach is used in which each hour under 2,000,000 is considered 5 times worse than each unskilled hour that exceeds the skilled hours, which in turn is 2 times worse than each skilled hour above 800,000.

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Q 52Q 52

It costs Extel $25 per chip to make its E86 chip used in notebook and other personal computers.Extel can sell all the chips it manufactures using a unit pricing model of ($60 - $0.01X) where X is the daily production of the chip.Fixed daily production costs are $700.

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Q 53Q 53

Fred Salter has a budget of $40,000 to prepare his house for sale.Fred's yard needs work, and the kitchen and bathroom could both use improvement.Fred has estimated the costs and expected return (increase in the value of his house) of different options.The cost and return are expressed in thousands of dollars.Fred wants to use dynamic programming to solve the problem.

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