Question 1

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

Accepted Answer

A) True 
 B)False  False

Question 2

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

Accepted Answer

(Dynamic programming requires a small fraction of the work needed for total enumeration.)

Question 3

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.A.Formulate this problem as a nonpreemptive goal programming model.
B.What is the optimal allocation of hours for this situation.

Accepted Answer

A.(MIN 10U₁ + 2U₂ + E₃
S.T.7.20X₁ + 12X₂ ? 28,800,000
X₁ + X₂ + U₁ - E₁ = 2,000,000
-X₁ + X₂ + U₂ - E₂ = 0
X₂ + U₃ - E₃ = 800,000
X₁, X₂, U₁, U₂, U₃, E₁, E₂, E₃ ? 0 )

B.(1,000,000 unskilled hours, 1,000,000 skilled hours.)

Question 4

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

Accepted Answer

A) True 
 B)False

Question 5

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.

Accepted Answer

A) True 
 B)False

Question 6

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

Accepted Answer

A) True 
 B)False

Question 7

The objective of goal programming is a solution that:

Accepted Answer

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. 
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.

Question 8

Quadratic programming is a special case of __________ programming.

Accepted Answer

A) standard linear 
B) general nonlinear 
C) goal 
D) dynamic 
A) standard linear 
B) general nonlinear 
C) goal 
D) dynamic

Question 9

Fred Salter has a budget of $40,000 to prepare his house for sale.Fred's yard needs work, and the kitchen and bathroom could both use improvement.Fred has estimated the costs and expected return (increase in the value of his house) of different options.The cost and return are expressed in thousands of dollars.Fred wants to use dynamic programming to solve the problem.$\begin{array}{ll}
\text { ROOM}&\text {PROJECT}&\text { COST}&\text { RETURN} \
\text { YARD}&\text { Seed lawn \& plant shrubs } & 2&2 \
&\text { Re-sod } & 5&8 \
&\text { Plant trees } & 15 &20\
\text { KITCHEH}&\text { Reface cabinets } & 10 &12\
&\text { New cabinets } & 25&40 \
&\text { Tile Floor } & 15&20 \
\text { BATHR00M}&\text { Refinish } & 5&10 \
&\text { Replace tile } & 10&18 \
&\text { New toilet, tub, \& plumbing } & 20&31
\end{array}$
 A.Define the stage variables.
B.Define the state variables.
C.Define the decision variables.
D.Define the stage return values.
E.Define the optimal value function.
F.Define the boundary condition.
G.Define the stopping rule.
H.Define the recurrence relation.
I.Solve the problem.

Accepted Answer

A.(The "rooms," which includes the yard

Question 10

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

Accepted Answer

(Results: Stage 3: F₃(4) = 17, F₃(3) = 25,

Question 11

What is "dynamic" about a dynamic programming problem?

Accepted Answer

(It is dynamic in the sense of being non

Question 12

The fundamental approach to solving dynamic programming problems may be characterized as:

Accepted Answer

A) forward incursion. 
B) backwards recursion. 
C) total enumeration. 
D) networking. 
A) forward incursion. 
B) backwards recursion. 
C) total enumeration. 
D) networking.

Question 13

In a goal programming model in which goal 1 has a higher priority than goal 2:

Accepted Answer

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. 
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.

Question 14

Consider the problem faced by Terrestrial Telescopes in problem 2.A.What is the optimal allocation of the weekly budget between salaries and equipment?
B.How many Orion telescopes can be made weekly?
C.What is the value (in terms of extra telescopes produce) of
(i) only raising the overall budget?
 (ii) only raising the maximum allocation for machinery?
D.Other than solving the Kuhn-Tucker conditions by trial and error,
what is another solution approach for solving this model?

Accepted Answer

A.(Solving the Kuhn-Tucker conditions b

Question 15

A knapsack problem can be modeled as a longest path network problem.

Accepted Answer

A) True 
 B)False

Question 16

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

Accepted Answer

A) True 
 B)False

Question 17

Which of the following need not be part of a dynamic programming model?

Accepted Answer

A) Linear constraints. 
B) Boundary conditions. 
C) A return function for each possible decision at each stage. 
D) An optimal value function. 
A) Linear constraints. 
B) Boundary conditions. 
C) A return function for each possible decision at each stage. 
D) An optimal value function.

Question 18

Variables raised to a power other than 1, may be found in a nonlinear programming problem.Other nonlinearities include:

Accepted Answer

A) cross products, but not quotients. 
B) quotients, but not cross products. 
C) either cross products or quotients. 
D) neither cross products nor quotients. 
A) cross products, but not quotients. 
B) quotients, but not cross products. 
C) either cross products or quotients. 
D) neither cross products nor quotients.

Question 19

For general nonlinear programming problems, the Kuhn-Tucker conditions:

Accepted Answer

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. 
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.

Question 20

What differentiates preemptivefrom nonpreemptive goal
programming?

Accepted Answer

(In both cases, the multiple goals must

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

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

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

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.

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

The objective of goal programming is a solution that:

Quadratic programming is a special case of __________ programming.

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

What is "dynamic" about a dynamic programming problem?

The fundamental approach to solving dynamic programming problems may be characterized as:

In a goal programming model in which goal 1 has a higher priority than goal 2:

A knapsack problem can be modeled as a longest path network problem.

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

Which of the following need not be part of a dynamic programming model?

Variables raised to a power other than 1, may be found in a nonlinear programming problem.Other nonlinearities include:

For general nonlinear programming problems, the Kuhn-Tucker conditions:

What differentiates preemptivefrom nonpreemptive goal programming?

Introduction to Management Science Models

Introduction to Management Science Models

Applications of Linear and Integer Programming Models

Network Models

Project Scheduling Models

Decision Models

Forecasting

Inventory Models

Queuing Models

Simulation Models

Quality Management Models

Markov Process Models

Filters

Exam 13: Nonlinear Models:dynamic, Goal, and Nonlinear Programming

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

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

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

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.

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

The objective of goal programming is a solution that:

Quadratic programming is a special case of __________ programming.

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

What is "dynamic" about a dynamic programming problem?

The fundamental approach to solving dynamic programming problems may be characterized as:

In a goal programming model in which goal 1 has a higher priority than goal 2:

A knapsack problem can be modeled as a longest path network problem.

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

Which of the following need not be part of a dynamic programming model?

Variables raised to a power other than 1, may be found in a nonlinear programming problem.Other nonlinearities include:

For general nonlinear programming problems, the Kuhn-Tucker conditions:

What differentiates preemptivefrom nonpreemptive goal programming?

Introduction to Management Science Models

Introduction to Management Science Models

Applications of Linear and Integer Programming Models

Network Models

Project Scheduling Models

Decision Models

Forecasting

Inventory Models

Queuing Models

Simulation Models

Quality Management Models

Markov Process Models

Filters