Question 1

What is the Principle of Optimality, and what is its relationship to Dynamic Programming?

Accepted Answer

The answer of What is the Principle of Optimality, and...

Question 2

A driver wants to make a trip from city 1 to city 7. The road mileage between cities is given below. Find the shortest route. $$\begin{array} { c | c c c c c c c } 
\text { From } & & { \text { To City: } } \
\text { City: } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline 1 & - & 2 & 2 & 4 & - & - & - \
2 & - & - & - & - & -4 & 10 & - \
3 & - & - & - & - & 12 & 6 & - \
4 & - & - & - & - & 10 & - & - \
5 & - & - & - & - & - & - & 14 \
6 & - & - & - & - & - & - & 2 \
7 & - & - & - & - & - & - & -
\end{array}$$

Accepted Answer

The answer of A driver wants to make a trip...

Question 3

Consider the following integer linear program Max 5x₁ + 7x₂ + 9x₃ s.t. 2x₁ + 3x₂ + 4x₃ $\le$ 8 x₁ $\le$ 3 x₂ $\le$2 x₁, x₂, x₃ $\ge$ 0, integer a.Set up the network that represents the dynamic programming formulation. b.Solve the problem using dynamic programming.

Accepted Answer

The answer of Consider the following integer linear program Max 5x₁ +...

Question 4

A stage in a dynamic programming problem is defined when 2 variables and 2 functions related to that stage are defined. Identify and define the 2 variables and 2 functions and illustrate them with an example of your choice.

Accepted Answer

The answer of A stage in a dynamic programming problem...

Question 5

The owner of a small construction firm is excavating at three sites. He wishes to assign his 5 additional trucks in such a way as to minimize his total costs. Each site can use 0 to 3 additional trucks; no site can use more than 3 trucks efficiently. The following site total costs are known. $$\begin{array} { c | r c c } 
\text { Number } && { \text { Cost of Excavating } } \
\text { of Trucks }& \text { Site 1 }& \text { Site 2 }& \text { Site 3 }\
\hline 0 & \$ 10000 & \$ 15000 & \$ 20000  \
 1 & 10000 & 14000 & 18000 \
2 & 9200 & 13250 & 17500 \
3 & 8500 & 12750 & 17250
\end{array}$$ 
a.Use dynamic programming to find the assignment of the additional trucks that minimizes total cost.
b.If the owner had only 4 trucks to assign, what would be the optimal assignment and total cost?

Accepted Answer

The answer of The owner of a small construction firm...

Question 6

A cargo company has a set of delivery patterns for its goods from its locations at city1 to a series of cities 2,3,4,5, and 6. The delivery times between cities are given I hours below. Find the shortest route. $$\begin{array} { c | c c c c c c c } 
\text { From } & { \text { To City: } } \
\text { City: } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline 1 & - & 6 & 10 & 7 & - & - & - \
2 & 6 & - & 4 & - & 5 & - & - \
3 & 10 & 4 & - & 4 & 2 & 4 & - \
4 & 7 & - & 5 & - & - & 8 & - \
5 & - & 5 & 3 & - & - & - & 7 \
6 & - & - & 4 & 8 & - & - & 5 \
7 & - & - & - & - & 7 & 5 & -
\end{array}$$

Accepted Answer

The answer of A cargo company has a set of...

Question 7

We have a number of types of items to be shipped as cargo. The total available weight in the truck is ten tons. We wish to determine the number of units of items to be shipped to maximize profit. $$\begin{array} { c c c } 
\text { Item } & \text { Weight (Tons) } & \text { Profit (1000s dollars) } \
\text { A } & 3 & 5 \
\text { B } & 4 & 7 \
\text { C } & 2 & 3
\end{array}$$

Accepted Answer

The answer of We have a number of types of...

Question 8

Audio Disks will be opening outlets in the greater Phoenix area. The estimated sales at each store are dependent not only on the store location, but on the number of sales personnel, as presented in the table below ($000/year). Each store requires at least 2 sales people, and a pool of 9 salespeople is available. $$\begin{array} { c | c c c c } 
& { \text { Staff Size } } \
& 2 & 3 & 4 & 5 \
\hline \text { Store 1 } & 60 & 85 & 90 & 100 \
\text { Store 2 } & 105 & 120 & 130 & 150 \
\text { Store 3 } & 120 & 145 & 160 & 175
\end{array}$$ 
a.What would the states be in the dynamic programming formulation?
b.Draw the network that represents the dynamic programming formulation.
c.Given the above network, solve the sales personnel allocation problem by finding the longest path.

Accepted Answer

The answer of Audio Disks will be opening outlets in...

Question 9

Define the following terms as they relate to dynamic programming.
a.Stage.
b.State variable.
c.Stage transformation function.

Accepted Answer

The answer of Define the following terms as they relate...

Question 10

Find the shortest path through the following network using dynamic programming.

Accepted Answer

The answer of Find the shortest path through the following...

Quiz 21: Dynamic Programming

What is the Principle of Optimality, and what is its relationship to Dynamic Programming?

Consider the following integer linear program Max 5x₁ + 7x₂ + 9x₃ s.t. 2x₁ + 3x₂ + 4x₃ $\le$ 8 x₁ $\le$ 3 x₂ $\le$ 2 x₁, x₂, x₃ $\ge$ 0, integer a.Set up the network that represents the dynamic programming formulation. b.Solve the problem using dynamic programming.

A stage in a dynamic programming problem is defined when 2 variables and 2 functions related to that stage are defined. Identify and define the 2 variables and 2 functions and illustrate them with an example of your choice.

Define the following terms as they relate to dynamic programming. a.Stage. b.State variable. c.Stage transformation function.

Find the shortest path through the following network using dynamic programming.

Quiz 21: Dynamic Programming

What is the Principle of Optimality, and what is its relationship to Dynamic Programming?

Consider the following integer linear program Max 5x1 + 7x2 + 9x3 s.t. 2x1 + 3x2 + 4x3 ≤\le≤ 8 x1 ≤\le≤ 3 x2 ≤\le≤ 2 x1, x2, x3 ≥\ge≥ 0, integer a.Set up the network that represents the dynamic programming formulation. b.Solve the problem using dynamic programming.

A stage in a dynamic programming problem is defined when 2 variables and 2 functions related to that stage are defined. Identify and define the 2 variables and 2 functions and illustrate them with an example of your choice.

Define the following terms as they relate to dynamic programming. a.Stage. b.State variable. c.Stage transformation function.

Find the shortest path through the following network using dynamic programming.

Consider the following integer linear program Max 5x₁ + 7x₂ + 9x₃ s.t. 2x₁ + 3x₂ + 4x₃ $\le$ 8 x₁ $\le$ 3 x₂ $\le$ 2 x₁, x₂, x₃ $\ge$ 0, integer a.Set up the network that represents the dynamic programming formulation. b.Solve the problem using dynamic programming.