Question 1

LO1: Develop and solve nonlinear optimization models for different applications. Use the table below to answer the following questions).
Pickson Luthiers Corporation is studying where to locate a phone charging point on the factory floor. The locations of five production cells are expressed as X- and Y-coordinates on a rectangular grid of the factory layout. The daily demand for the charging point measured as the number of trips to the charging point) at each production cell is also known. Because of the nature of the equipment layout in the factory and for safety reasons, workers must travel along marked horizontal and vertical aisles to access the charger. Thus, the distance from a cell to the charger is measured as rectilinear distance.
The table below provides the relevant information. $\begin{array}{|l|l|l|l|}
\hline\text { Pickson Luthiers } \ \text { Corporation } & \text { Phone Recharging Points }  & \
\hline & & & \
\hline \text { Data }  & \
\hline\
\hline \text { Cell } & X \text {-coordinate } & Y \text {-coordinate } & \text { Demand } \
\hline \text { Measurements } & 2 & 5 & 27 \
\hline \text { Paint } & 1 & 3 & 12 \
\hline \text { Electricals } & 4 & 2 & 25 \
\hline
\end{array}$ $$\begin{array} { | l | l | l | l | } 
\hline \text { Testing } & 3.5 & 5 & 5 \
\hline \text { Packnging } & 3 & 3 & 7 \
\hline & & & \
\hline \text { Maxirnum } & 4 & 5 & \
\hline
\end{array}$$ The optimal location should minimize the total weighted distance between the charging point and all production cells, where the weights are the daily number of trips to the phone charging point.
Create a nonsmooth optimization model, based on the data, to answer the following questions. Hint: Choose the closest answers.)
-According to the model, which of the following is the weighted distance between the phone charger and Packaging cell?
A) 10.50
B) 0
C) 7.00
D) 14.00

Accepted Answer

The weighted distance between the phone charger and a cell is calculated by multiplying the rectilinear distance by the cell's demand. For the Packaging cell, with coordinates (3,3) and a demand of 7, if we assume the charger is placed optimally but without knowing its exact location, we can't calculate the exact distance. However, the question seems to ask for the formula to calculate this distance, which would be the rectilinear distance (difference in x plus difference in y coordinates) times the demand. Without the charger's location, we can't provide a numerical answer, but the correct approach involves multiplying the demand by the rectilinear distance to the charger. The given options don't align with this explanation due to the lack of specific charger location, but the principle to find the weighted distance is to use the demand as a weight.

Question 2

LO1: Develop and solve nonlinear optimization models for different applications. Use the table below to answer the following questions).
Pickson Luthiers Corporation is studying where to locate a phone charging point on the factory floor. The locations of five production cells are expressed as X- and Y-coordinates on a rectangular grid of the factory layout. The daily demand for the charging point measured as the number of trips to the charging point) at each production cell is also known. Because of the nature of the equipment layout in the factory and for safety reasons, workers must travel along marked horizontal and vertical aisles to access the charger. Thus, the distance from a cell to the charger is measured as rectilinear distance.
The table below provides the relevant information. $\begin{array}{|l|l|l|l|}
\hline\text { Pickson Luthiers } \ \text { Corporation } & \text { Phone Recharging Points }  & \
\hline & & & \
\hline \text { Data }  & \
\hline\
\hline \text { Cell } & X \text {-coordinate } & Y \text {-coordinate } & \text { Demand } \
\hline \text { Measurements } & 2 & 5 & 27 \
\hline \text { Paint } & 1 & 3 & 12 \
\hline \text { Electricals } & 4 & 2 & 25 \
\hline
\end{array}$ $$\begin{array} { | l | l | l | l | } 
\hline \text { Testing } & 3.5 & 5 & 5 \
\hline \text { Packnging } & 3 & 3 & 7 \
\hline & & & \
\hline \text { Maxirnum } & 4 & 5 & \
\hline
\end{array}$$ The optimal location should minimize the total weighted distance between the charging point and all production cells, where the weights are the daily number of trips to the phone charging point.
Create a nonsmooth optimization model, based on the data, to answer the following questions. Hint: Choose the closest answers.)
-According to the model, what is the total weighted distance between the 5 production cells and the phone charger?
A) 253.50
B) 113.00
C) 172.50
D) 165.50

Accepted Answer

The answer of LO1: Develop and solve nonlinear optimization models...

Question 3

Rectilinear distance is the measure of distance as a straight line between two points.

Accepted Answer

Rectilinear distance, also known as Manhattan distance, measures the distance between two points by only moving along grid lines, not in a straight line.

Question 4

The economic order quantity is the amount to order that minimizes the total cost of ordering and holding.

Accepted Answer

The Economic Order Quantity (EOQ) model is designed to help businesses minimize the total cost associated with ordering and holding inventory by determining the most efficient order quantity.

Question 5

All Nonlinear Optimization Models models have nonlinear constraints.

Accepted Answer

Nonlinear optimization models may have a mix of linear and nonlinear constraints, or even exclusively linear constraints; the nonlinearity can stem from the objective function.

Question 6

LO1: Develop and solve nonlinear optimization models for different applications. Use the table below to answer the following questions).
Pickson Luthiers Corporation is studying where to locate a phone charging point on the factory floor. The locations of five production cells are expressed as X- and Y-coordinates on a rectangular grid of the factory layout. The daily demand for the charging point measured as the number of trips to the charging point) at each production cell is also known. Because of the nature of the equipment layout in the factory and for safety reasons, workers must travel along marked horizontal and vertical aisles to access the charger. Thus, the distance from a cell to the charger is measured as rectilinear distance.
The table below provides the relevant information. $\begin{array}{|l|l|l|l|}
\hline\text { Pickson Luthiers } \ \text { Corporation } & \text { Phone Recharging Points }  & \
\hline & & & \
\hline \text { Data }  & \
\hline\
\hline \text { Cell } & X \text {-coordinate } & Y \text {-coordinate } & \text { Demand } \
\hline \text { Measurements } & 2 & 5 & 27 \
\hline \text { Paint } & 1 & 3 & 12 \
\hline \text { Electricals } & 4 & 2 & 25 \
\hline
\end{array}$ $$\begin{array} { | l | l | l | l | } 
\hline \text { Testing } & 3.5 & 5 & 5 \
\hline \text { Packnging } & 3 & 3 & 7 \
\hline & & & \
\hline \text { Maxirnum } & 4 & 5 & \
\hline
\end{array}$$ The optimal location should minimize the total weighted distance between the charging point and all production cells, where the weights are the daily number of trips to the phone charging point.
Create a nonsmooth optimization model, based on the data, to answer the following questions. Hint: Choose the closest answers.)
-According to the model, which of the following is the weighted distance between the phone charger and Testing cell?
A) 7.00
B) 17.50
C) 22.50
D) 27.50

Accepted Answer

The weighted distance between the phone charger and the Testing cell is calculated by multiplying the rectilinear distance by the daily demand (number of trips). Given the coordinates of the Testing cell (3.5, 5) and assuming the charger is placed at the optimal location (which is not specified in the question), we can't calculate the exact distance without knowing the charger's location. However, the closest answer, considering the nature of the question and the hint to choose the closest answers, would be to consider the distance as the product of the demand and a unit distance, which gives us 5 trips * 3.5 units (assuming a unit distance for simplicity since the exact location of the charger is unknown) = 17.50 as the closest approximation.

Question 7

Explain how the Markowitz portfolio model is a Nonlinear Optimization Models model.

Accepted Answer

The answer of Explain how the Markowitz portfolio model is...

Question 8

What is a job-sequencing problem? How can we find an optimal solution for such problems?

Accepted Answer

The answer of What is a job-sequencing problem? How can...

Question 9

LO1: Develop and solve nonlinear optimization models for different applications. Use the table below to answer the following questions).
Pickson Luthiers Corporation is studying where to locate a phone charging point on the factory floor. The locations of five production cells are expressed as X- and Y-coordinates on a rectangular grid of the factory layout. The daily demand for the charging point measured as the number of trips to the charging point) at each production cell is also known. Because of the nature of the equipment layout in the factory and for safety reasons, workers must travel along marked horizontal and vertical aisles to access the charger. Thus, the distance from a cell to the charger is measured as rectilinear distance.
The table below provides the relevant information. $\begin{array}{|l|l|l|l|}
\hline\text { Pickson Luthiers } \ \text { Corporation } & \text { Phone Recharging Points }  & \
\hline & & & \
\hline \text { Data }  & \
\hline\
\hline \text { Cell } & X \text {-coordinate } & Y \text {-coordinate } & \text { Demand } \
\hline \text { Measurements } & 2 & 5 & 27 \
\hline \text { Paint } & 1 & 3 & 12 \
\hline \text { Electricals } & 4 & 2 & 25 \
\hline
\end{array}$ $$\begin{array} { | l | l | l | l | } 
\hline \text { Testing } & 3.5 & 5 & 5 \
\hline \text { Packnging } & 3 & 3 & 7 \
\hline & & & \
\hline \text { Maxirnum } & 4 & 5 & \
\hline
\end{array}$$ The optimal location should minimize the total weighted distance between the charging point and all production cells, where the weights are the daily number of trips to the phone charging point.
Create a nonsmooth optimization model, based on the data, to answer the following questions. Hint: Choose the closest answers.)
-According to the model, which of the following production cells covers the most distance according to its demand when using the phone charger?
A) Measurements
B) Paint
C) Electricals
D) Testing

Accepted Answer

The optimal location for the charging point minimizes the total weighted distance, which depends on both the distance to each cell and the demand from that cell. The Electricals cell has a high demand (25 trips) and is located relatively far from the other cells (X=4, Y=2), which likely makes it cover the most distance according to its demand when using the phone charger, especially when considering rectilinear distance in a layout where movement is restricted to horizontal and vertical aisles.

Question 10

Pickson Luthiers Corporation is studying where to locate a phone charging point on the factory floor. The locations of five production cells are expressed as X- and Y-coordinates on a rectangular grid of the factory layout. The daily demand for the charging point measured as the number of trips to the charging point) at each production cell is also known. Because of the nature of the equipment layout in the factory and for safety reasons, workers must travel along marked horizontal and vertical aisles to access the charger. Thus, the distance from a cell to the charger is measured as rectilinear distance.
The table below provides the relevant information. $\begin{array}{|l|l|l|l|}
\hline \begin{array}{l}
\text { Pickson Luthiers } \
\text { Corporation }
\end{array} & \text { Phone Recharging Points } & & \
\hline & & & \
\hline \text { Data } & & & \\hline \
\hline \text { Cell } & X \text {-coordinate } & Y \text {-coordinate } & \text { Demand } \
\hline \text { Measurements } & 2 & 5 & 27 \
 \hline \text { Paint } & 1 & 3 & 12 \
\hline \text { Electricals } & 4 & 2 & 25 \
\hline \text { Testing } & 3.5 & 5 & 5 \
\hline \text { Packaging } & 3 & 3 & 7 \
\hline & & & \
\hline \text { Maximum } & 4 & 5 &\
\hline
\end{array}$ The optimal location should minimize the total weighted distance between the charging point and all production cells, where the weights are the daily number of trips to the phone charging point.
From the above table, provide the objective function for the best location of the charging point. What kind of solution technique from Solver can be used to make the optimization model based on the data?

Accepted Answer

The answer of Pickson Luthiers Corporation is studying where to...

Question 11

Jonathan Reese is considering three stocks in which to invest with a fixed budget. The table below provides information on Jonathan's expected returns for each stock. The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks. He expects a total return of at least 10%. $$\begin{array} { | l | c | l | l | l | l | l | } 
\hline \begin{array} { l } 
\text { Reese's Stock } \
\text { Investment } \
\text { Plan }
\end{array} & & & & & & \
\hline & & & & & & \
\hline \text { Data } & & & & & \
\hline & \text { Expected } & & &{ \text { Variance-Covariance Matrix } } \
\hline & \text { Return } & & & \text { Stock 1 } & \text { Stock 2 } & \text { Stock 3 } \
\hline \text { Stock 1 } & 10 \% & & \text { Stock 1 } & 0.021 & 0.018 & - 0.003 \
\hline \text { Stock 2 } & 11 \% & & \text { Stock 2 } & 0.018 & 0.070 & 0.006 \
\hline \text { Stock 3 } & 9 \% & & \text { Stock 3 } & - 0.003 & 0.006 & 0.003 \
\hline \begin{array} { l } 
\text { Target } \
\text { Retum }
\end{array} & 10 \% & & & & & \
\hline
\end{array}$$ Using the table above, provide the objective function for minimal variance, and the constraints for creating an optimization model.

Accepted Answer

The answer of Jonathan Reese is considering three stocks in...

Question 12

Absolute value functions, in optimization models, result in non-smooth functions.

Accepted Answer

Absolute value functions create a kink at the point where their argument is zero, leading to a non-smooth or non-differentiable point, which complicates optimization processes that rely on smoothness.

Question 13

Explain the travelling salesperson problem with examples.

Accepted Answer

The answer of Explain the travelling salesperson problem with examples....

Quiz 14: Integer and Nonlinear Optimization Models