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

Question

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

Quizplus · 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.

LO1: Develop and Solve Nonlinear Optimization Models for Different Applications