Deck 17: Dynamic Programming

Question 1

There are six cities (City 1-City 6)serviced by a particular bus line.Limited routes are available,and the distance for each of these routes is presented in the table below.
If dynamic programming were used to solve for the minimum distance from City 1 to City 6 above,how many stages would there be?

A)6
B)5
C)4
D)3
E)2

Answer 1

D

Question 2

In dynamic programming,the decision rules defining an optimal policy give optimal decisions for any entering condition at any stage.

Answer 2

True

Question 3

The second step in solving a dynamic programming problem is to solve the last stage of the problem for all conditions or states.

Answer 3

True

Question 4

Dynamic programming can be applied to a professional tennis player's serving strategy.

Question 5

For the bus line problem above,what are the stages that provide the minimum distance?

A)1-2,2-4,4-6
B)1-2,2-5,5-6
C)1-3,3-4,4-6
D)1-3,3-5,5-6
E)None of the above

Question 6

Your local paper carrier could make use of the shortest-route technique.

Question 7

The following information describes a shortest-route problem with the distance in miles.How many stages will this dynamic problem have?

A)8
B)4
C)3
D)2
E)1

Question 8

In a shortest-route problem,the nodes represent the destinations.

Question 9

In dynamic programming,there is a state variable defined for every stage.

Question 10

Both dynamic programming and linear programming take a multi-stage approach to solving problems.

Question 11

Table M2-1
The data below is a dynamic programming solution for a shortest route problem.
Using the data in Table M2-1,determine the minimum distance from point 1 to point 7.

A)21
B)22
C)23
D)24
E)75

Question 12

Each item in a knapsack problem will be a stage of the dynamic programming problem.

Question 13

Dynamic programming can only be used to solve network-based problems.

Question 14

A transformation changes the identities of the state variables.

Question 15

Linear programming is typically applied to problems wherein one must make a decision at a specified point (or points)in time.Dynamic programming is typically applied to problems wherein one must make a sequence of decisions.

Question 16

Subproblems in a dynamic programming problem are called stages.

Question 17

For the bus line problem above,what is the minimum possible distance to travel from City 1 to City 6?

A)26
B)20
C)18
D)22
E)None of the above

Question 18

For knapsack problems,s_n-1 = a_n × s_n + b_n × d_n + c_n is a typical transformation expression.

Question 19

In a shortest-route problem,the limit on the number of allowable decision variables from one node to another is the number of possible nodes to which one might yet travel.

Question 20

The problem that NASA has in determining what types of cargo may be loaded on the space shuttle is an example of a knapsack problem.

Question 21

If the truck were required to take the route from City 4 to City 5,what would be the overall route?

A)1-3,3-4,4-5,5-6,6-7
B)1-2,2-4,4-5,5-7
C)1-2,2-3,3-4,4-5,5-6,6-7
D)1-3,3-5,5-6,6-7
E)None of the above

Question 22

here are six cities (City 1-City 6)serviced by a particular airline.Limited routes are available,and the distances for each of these routes are presented in the table below.
What is the minimum distance that must be traveled to get from City 1 to City 6?

A)9
B)10
C)11
D)12
E)None of these

Question 23

The following information is to be used for the questions below:
There are seven cities (City 1-City 7)served by Acme Trucking.Route availability is limited.The distances,in hundreds of miles,are given in the table below for each route.
What route should the truck from City 1 to City 7 take?

A)1-2,2-5,5-7
B)1-3,3-4,4-6,6-7
C)1-2,2-4,4-5,5-6,6-7
D)1-3,3-5,5-6,6-7
E)None of the above

Question 24

Table M2-3
For the shortest route problem described in Table M2-3,what is the distance for the shortest route?

A)155 miles
B)66 miles
C)59 miles
D)114 miles
E)None of the above

Question 25

Table M2-2
According to Table M2-2,which gives a solution to a shortest route problem solved with dynamic programming,which cities would be included in the best route?

A)1,2,3,4,5,6
B)1,4,6,7
C)1,2,5,6,7
D)6,7
E)None of the above

Question 26

Table M2-1
The data below is a dynamic programming solution for a shortest route problem.
Using the data in Table M2-1,what is the optimal travel path from point 1 to 7?

A)5,7
B)6,7
C)1,2,6,7
D)1,2,5,7
E)1,3,6,7

Question 27

A transformation describes

A)the relationship between stages.
B)the initial condition of the system.
C)a stage.
D)a state variable.
E)None of the above

Question 28

Table M2-1
The data below is a dynamic programming solution for a shortest route problem.
Using the data in Table M2-1,what is the optimal arc of stage 3?

A)1
B)1 - 4
C)1 - 3
D)1 - 2
E)None of the above

Question 29

Table M2-1
The data below is a dynamic programming solution for a shortest route problem.
Using the data in Table M2-1,determine the distance of stage 1 for the optimal route.

A)0
B)8
C)12
D)16
E)24

Question 30

Table M2-3
The above information describes a shortest-route problem with the distance in miles.How many stages will this dynamic programming problem have?

A)8
B)4
C)3
D)2
E)1

Question 31

Table M2-1
The data below is a dynamic programming solution for a shortest route problem.
Using the data in Table M2-1,determine the distance of stage 2 for the optimal route.

A)0
B)4
C)8
D)12
E)21

Question 32

Table M2-1
The data below is a dynamic programming solution for a shortest route problem.
Using the data in Table M2-1,determine the optimal arc of stage 1.

A)5
B)6
C)7
D)6 - 7
E)5 - 7

Question 33

The following information is to be used for the questions below:
GATRA,the Greater Attleboro-Taunton Regional Transit Authority serves six cities (City 1-City 6).While there are many restrictions (primarily roads on which they may not travel),they do have some choice of routes.The distances between cities,along permitted routes,are presented below.
What is the minimum distance that must be traveled to get from City 1 to City 6?

A)26
B)9
C)11
D)3
E)None of these

Question 34

Table M2-1
The data below is a dynamic programming solution for a shortest route problem.
Using the data in Table M2-1,determine the optimal arc of stage 2.

A)4 - 6
B)3 - 6
C)3 - 5
D)2 - 6
E)2 - 5

Question 35

The following information is to be used for the questions below:
There are seven cities (City 1-City 7)served by Acme Trucking.Route availability is limited.The distances,in hundreds of miles,are given in the table below for each route.
What is the minimum distance a load being moved from City 1 to City 7 must travel?

A)3000 miles
B)2900 miles
C)1500 miles
D)2700 miles
E)None of the above

Question 36

Table M2-2
According to Table M2-2,which gives a solution to a shortest route problem solved with dynamic programming,the total distance from City 1 to City 7 is 14.What is the shortest distance from City 3 to City 7?

A)7
B)10
C)13
D)25
E)None of these

Question 37

A stage is a(n)

A)alternative.
B)policy.
C)condition at the end of the problem.
D)subproblem.
E)None of the above

Question 38

If the truck were required to take the route from City 4 to City 5,what would be the shortest distance from City 1 to City 7?

A)2900 miles
B)3200 miles
C)3700 miles
D)3400 miles
E)None of the above

Question 39

Table M2-1
The data below is a dynamic programming solution for a shortest route problem.
Using the data in Table M2-1,determine the distance of stage 3 for the optimal route.

A)22
B)23
C)24
D)7
E)10

Question 40

The following information is to be used for the questions below:
GATRA,the Greater Attleboro-Taunton Regional Transit Authority serves six cities (City 1-City 6).While there are many restrictions (primarily roads on which they may not travel),they do have some choice of routes.The distances between cities,along permitted routes,are presented below.
What is the shortest route?

A)1-3,3-5,5-6
B)1-2,2-3,3-4,4-5,5-6
C)1-3,3-4,4-5,5-6
D)1-2,2-3,3-5,5-6
E)None of the above

Question 41

Table M2-3
For the shortest route problem described in Table M2-3,which arcs comprise the shortest route?

A)1-2,2-6,6-8
B)1-5,5-8
C)1-2,2-5,5-8
D)1-3,3-5,5-8
E)None of the above

Question 42

For the questions which follow,there are six cities (City 1-City 6)serviced by a particular airline.Limited routes are available,and the distances for each of these routes are presented in the table below.
What is the minimum distance that must be traveled to get from City 1 to City 6?

A)1100 miles
B)900 miles
C)1,300 miles
D)1,400 miles
E)None of the above

Question 43

Table M2-4
For the shortest route problem described in Table M2-4,what is the length of the shortest route?

A)205 miles
B)94 miles
C)241 miles
D)108 miles
E)None of the above

Question 44

Develop the shortest-route network for the problem below,and determine the minimum distance from node 1 to node 7.

Question 45

The data below details the distances that a delivery service must travel.Use dynamic programming to solve for the shortest route from City 1 to City 8.

Question 46

Table M2-5
The data below is a dynamic programming solution for a shortest route problem.
Using the data in Table M2-5,determine the optimal distance of stage 1.

A)0
B)8
C)7
D)14
E)None of the above

Question 47

Table M2-5
The data below is a dynamic programming solution for a shortest route problem.
Using the data in Table M2-5,determine the optimal arc of stage 2.

A)4 - 6
B)5 - 6
C)4 - 5
D)2 - 5
E)None of the above

Question 48

Table M2-5
The data below is a dynamic programming solution for a shortest route problem.
Using the data in Table M2-5,determine the optimal distance of stage 3.

A)22
B)17
C)24
D)7
E)None of the above

Question 49

Table M2-5
The data below is a dynamic programming solution for a shortest route problem.
Using the data in Table M2-5,determine the optimal travel path from point 1 to point 7.

A)1 - 2,2 - 4,4 - 5,5 - 7
B)1 - 2,2 - 5,5 - 7
C)1 - 3,3 - 4,4 - 5,5 - 7
D)1 - 2,2 - 4,4 - 6,6 - 7
E)None of the above

Question 50

Develop the shortest-route network for the problem below,and determine the minimum distance from node 1 to node 8.

Question 51

What is meant by a decision variable in a shortest-route problem?

Question 52

Table M2-5
The data below is a dynamic programming solution for a shortest route problem.
Using the data in Table M2-5,determine the optimal arc of stage 4.

A)1 - 2
B)2 - 4
C)1 - 3
D)3 - 4
E)None of the above

Question 53

What is the decision criterion for a shortest route problem?

Question 54

Table M2-5
The data below is a dynamic programming solution for a shortest route problem.
Using the data in Table M2-5,determine the optimal distance of stage 2.

A)10
B)7
C)8
D)11
E)None of the above

Question 55

Hard D.Head has decided that he wants to climb one of the world's tallest mountains.He has mapped out a number of routes between various points on the mountain,and rated each route as to difficulty.His rating scale considers a 1 as being particularly easy,and a 10 as being almost impossible.
(a)Given the information below,identify the route that would provide the easiest climb.
(b)What would be the average rating of the route?
(c)What is wrong with this approach to Mr.Head's problem?

Question 56

Table M2-4
For the shortest route problem described in Table M2-4,which arcs comprise the shortest route?

A)1-2,2-6,6-8
B)1-3,3-5,5-8
C)1-5,5-8
D)1-2,2-4,4-7,7-8
E)None of the above

Question 57

Table M2-5
The data below is a dynamic programming solution for a shortest route problem.
Using the data in Table M2-5,determine the optimal arc of stage 1.

A)3 - 7
B)6 - 7
C)5 - 7
D)4 - 7
E)None of the above

Question 58

For the questions which follow,there are six cities (City 1-City 6)serviced by a particular airline.Limited routes are available,and the distances for each of these routes are presented in the table below.
Which routes should be traveled?

A)1-2,2-3,3-5,5-6
B)1-2,2-3,3-4,4-6
C)1-2,2-5,5-6
D)1-4,4-6
E)None of the above

Question 59

There are four items (A,B,C,and
D)that are to be shipped by air.The weights of these are 3,4,5,and 3 tons,respectively.The profits (in thousands of dollars)generated by these are 5 for A,6 for B,7 for C,and 6 for D.There are 2 units of A,1 unit of B,3 units of C,and 2 units of D available to be shipped.The maximum weight is 16 tons.Use dynamic programming to determine the maximum possible profits that may be generated.

Question 60

Table M2-5
The data below is a dynamic programming solution for a shortest route problem.
Using the data in Table M2-5,determine the minimum distance from point 1 to point 7.

A)18
B)17
C)23
D)14
E)None of the above

Question 61

Identify two types of problems that can be solved by dynamic programming.

Question 62

In the shortest-route problem,circles represent ________,and arrows represent ________.

Question 63

What are the four elements defining each stage in a dynamic programming problem?

Question 64

Discuss,briefly,the difference between a decision variable and a state variable.

Question 65

Discuss,briefly,the role of the transformation function.

Question 66

What is the decision criterion for a knapsack problem?

Question 67

What are the four steps in dynamic programming?