Refer to the Active Model Exercise provided at the end of Chapter $13$ on page $566$ of text. $[$Students should make use of the Microft Excel file is provided in Module $0,$ which consists setups of all Active Model Exercises.$]$ Please answer the following four questions related to the Active Model Exercise and submit your answers in the submission window. $($Please ensure to click on "Reset Data" button before attempting each question.$)$

In your submission, you do not need to rewrite the questions; just itemize the answers as #$1,$ #$2,$ etc. You will be graded based on the accuracy and completeness your answers.

Questions

What is the total load$$distance score to the new Health$-$Watch medical facility if it is located at the center of gravity?

Fix the y$-$coordinate $($that is$,$ keep the y$-$coordinate constant$),$ and use the scroll bar to modify the x$-$coordinate. Can you reduce the total load$$distance score?

Fix the x$-$coordinate, and use the scroll bar to modify the y$-$coordinate. Can you reduce the total load$$distance score?

The center of gravity does not necessarily find the site with the minimum total load$$distance score. Use both scroll bars to move the trial location, and see whether you can improve $($lower$)$ the total load$$distance score.Solved Problem $1$

The new Health$-$Watch facility is targeted to serve seven census tracts in Erie, Pennsylvania, whose latitudes and longitudes are shown in Table $13\mathrm{.}1,$ along with the population in each census tract $($in thousands$).$ Customers will travel from the seven census$-$tract centers to the new facility when they need health care. What is the target area's center of gravity for the Health$-$Watch medical facility?

TABLE $13\mathrm{.}1|$ LOCATION DATA AND CALCULATIONS FOR HEALTH$-$WATCH

$\backslash$table$[[$Census Tract,Population,Latitude,Longitude,Population $\backslash$times Latitude,Population $\backslash$times Longitude$],[15,2,711,42\mathrm{.}134,-80\mathrm{.}041,114,225\mathrm{.}27,-216,991\mathrm{.}15],[16,4,161,42\mathrm{.}129,-80\mathrm{.}023,175,298\mathrm{.}77,-332,975\mathrm{.}70],[17,2,988,42\mathrm{.}122,-80\mathrm{.}055,125,860\mathrm{.}54,-239,204\mathrm{.}34],[25,2,512,42\mathrm{.}112,-80\mathrm{.}066,105,785\mathrm{.}34,-201,125\mathrm{.}79],[26,4,342,42\mathrm{.}117,-80\mathrm{.}052,182,872\mathrm{.}01,-347,585\mathrm{.}78],[27,6,687,42\mathrm{.}116,-80\mathrm{.}023,281,629\mathrm{.}69,-535,113\mathrm{.}80],[28,6,789,42\mathrm{.}107,-80\mathrm{.}051,285,864\mathrm{.}42,-543,466\mathrm{.}24],[$Total$,30,190,,,1,271,536\mathrm{.}04,-2,416,462\mathrm{.}80]]$

SOLUTION

We solve for the center of gravity $x^{**}$ and $y^{**}.$ Because the coordinates are given as longitude and latitude, $x^{**}$ is the longitude and $y^{**}$ is the latitude for the center of gravity.

$x^{**}=\frac{1,271,536\mathrm{.}05}{30,190}=42\mathrm{.}1178$

$y^{**}=\frac{-2,416,462\mathrm{.}81}{30,190}=-80\mathrm{.}0418$Refer to the Active Model Exercise provided at the end of Chapter $13$ on page $566$ of text. $[$Students should make use of the Microft Excel file is provided in Module $0,$ which consists setups of all Active Model Exercises.$]$ Please answer the following four questions related to the Active Model Exercise and submit your answers in the submission window. $($Please ensure to click on "Reset Data" button before attempting each question.$)$

In your submission, you do not need to rewrite the questions; just itemize the answers as #$1,$ #$2,$ etc. You will be graded based on the accuracy and completeness your answers.

Questions

What is the total load$$distance score to the new Health$-$Watch medical facility if it is located at the center of gravity?

Fix the y$-$coordinate $($that is$,$ keep the y$-$coordinate constant$),$ and use the scroll bar to modify the x$-$coordinate. Can you reduce the total load$$distance score?

Fix the x$-$coordinate, and use the scroll bar to modify the y$-$coordinate. Can you reduce the total load$$distance score?

The center of gravity does not necessarily find the site with the minimum total load$$distance score. Use both scroll bars to move the trial location, and see whether you can improve $($lower$)$ the total load$$distance score.