LO1: Develop and Solve Nonlinear Optimization Models for Different Applications

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