Question 1

The arrow labeled S₂ in Figure M2.1 represents the output from stage 1.

Accepted Answer

The arrow labeled S₂ in Figure M2.1 represents the output from stage 1.

Question 2

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

Accepted Answer

Dynamic programming takes a multi-stage approach to solving problems by breaking them down into simpler subproblems and solving each subproblem just once, storing its solution. Linear programming, however, is a mathematical method for determining a way to achieve the best outcome in a given mathematical model and does not inherently involve a multi-stage approach to problem-solving.

Question 3

The arrow labeled D₂ in Figure M2.1 represents a disturbance.

Accepted Answer

False

Question 4

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.

Accepted Answer

Linear programming involves optimizing a linear objective function subject to linear constraints at a given point in time, while dynamic programming involves making a sequence of decisions based on a recursive formula. Therefore, the statement is true.

Question 5

Subproblems in a dynamic programming problem are called stages.

Accepted Answer

Subproblems in a dynamic programming problem are typically solved in stages, with each stage building upon the solutions from previous stages.

Question 6

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

Accepted Answer

In a shortest-route problem, the nodes generally represent the locations or points between the destinations. The goal is to find the shortest distance between two specific nodes or points.

Question 7

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

Accepted Answer

Dynamic programming can be used to determine a professional tennis player's optimal serving strategy by considering factors such as the ball's speed, spin, and placement, as well as the opponent's position and tendencies. By analyzing past performance data, the player can use dynamic programming to adjust their serving strategy and improve their chances of winning.

Question 8

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

Accepted Answer

In dynamic programming, a state variable is defined for every stage to keep track of the current state of the system being optimized.

Question 9

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.

Accepted Answer

The knapsack problem involves determining the optimal combination of items to pack in a limited space or capacity. The NASA cargo problem involves selecting the most essential and useful items to bring on a space mission within the limitations of the spacecraft's cargo hold. This is a knapsack problem because NASA must make choices about what to bring based on limited space and weight capacity.

Question 10

A transformation changes the identities of the state variables.

Accepted Answer

A transformation does not change the identities of the state variables; it may change their values or representations, but they remain the same variables.

Question 11

The formula s_n = t_n(s_n-1,d_n,r_n)allows us to go from one stage to the next in Figure M2.1.

Accepted Answer

The answer of The formula s_n = t_n(s_n-1,d_n,r_n)allows us to...

Question 12

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

Accepted Answer

Dynamic programming is a method for solving optimization problems by breaking them down into smaller sub-problems and building up a solution based on the optimal solutions to these sub-problems. In dynamic programming, the decision rules defining an optimal policy give optimal decisions for any entering condition at any stage.

Question 13

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

Accepted Answer

In a knapsack problem, the stages correspond to the incremental addition of items to the knapsack. Each item represents a decision that can be made at a particular stage, so each item is a stage in the dynamic programming algorithm.

Question 14

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.

Accepted Answer

In a shortest-route problem, the limit on the number of allowable decision variables from one node to another is typically determined by the number of adjacent nodes that can be reached from the current node. This limit may vary depending on the specific problem and the constraints involved, but it is usually not equal to the total number of possible nodes in the graph.

Question 15

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

Accepted Answer

In dynamic programming, we typically start solving the problem from the last stage and work our way backwards. So, the second step is to solve the last stage for all conditions or states before moving on to earlier stages.

Question 16

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

Accepted Answer

The answer of Your local paper carrier could make use...

Question 17

The arrow labeled S₁ in Figure M2.1 represents an output.

Accepted Answer

The arrow labeled S₁ in Figure M2.1 represents the output of the system.

Question 18

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

Accepted Answer

Dynamic programming can also be used to solve problems that involve optimization of a sequence of decisions, such as the knapsack problem or the longest common subsequence problem. While network-based problems are a common application of dynamic programming, they are not the only type.

Question 19

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

Accepted Answer

This is a typical transformation expression used in the dynamic programming approach to solve the 0/1 knapsack problem.

Question 20

In Figure M2.1 there is a function t₂ that is not depicted, that converts s₂ and d₂ to s₁.

Accepted Answer

The statement indicates that there is a function that exists and is not depicted in the figure, which converts inputs s₂ and d₂ to output s₁. Therefore, the statement is true.

Quiz 17: Dynamic Programming

The arrow labeled S2 in Figure M2.1 represents the output from stage 1.

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

The arrow labeled D2 in Figure M2.1 represents a disturbance.

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.

Subproblems in a dynamic programming problem are called stages.

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

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

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

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.

A transformation changes the identities of the state variables.

The formula sn = tn(sn-1,dn,rn)allows us to go from one stage to the next in Figure M2.1.

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

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

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.

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

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

The arrow labeled S1 in Figure M2.1 represents an output.

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

For knapsack problems, sn-1 = an × sn + bn × dn + cn is a typical transformation expression.

In Figure M2.1 there is a function t2 that is not depicted, that converts s2 and d2 to s1.

The arrow labeled S₂ in Figure M2.1 represents the output from stage 1.

The arrow labeled D₂ in Figure M2.1 represents a disturbance.

The formula s_n = t_n(s_n-1,d_n,r_n)allows us to go from one stage to the next in Figure M2.1.

The arrow labeled S₁ in Figure M2.1 represents an output.

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

In Figure M2.1 there is a function t₂ that is not depicted, that converts s₂ and d₂ to s₁.