Question

In case the Rectilinear distance is considered, find the optimal coordinates (X,Y) of new facility. Q2) Show and label the existing locations and the optimal location of new facility on a scatter chart.

Answer 1

Complete Question

The complete question is shown on the second uploaded image

Answer:

a

The optimal x coordinate is 50.76 and the optimal y coordinate is 46.34

b

The Scatter plot is shown on the second uploaded image

Explanation:

In this question we are given the annual demand and the annual cost per mile  per ton. Now to obtain the annual cost per mile for the whole inventory  we multiply the demand  with the cost per mile per ton.

This shown on the third uploaded image

To obtain the optimal new coordinate let consider the location of the existing coordinates and the annual cost of the existing facilities

   Mathematically the optimal x coordinate = (Summation of the old x coordinates multiplied by the annual cost per mile) /(Summation of the annual cost per mile  )

i.e optimal new x coordinate = $(40* 6250 +50*4400+70*9500 +25*4350)/(6250+4400+9500+4350)$

$=(250000+220000+665000+108750)/(24500) = 1243750/24500 = 50.76$  

 For y

the optimal y coordinate = (Summation of the old y coordinates multiplied by the annual cost per mile) /(Summation of the annual cost per mile  )

      $=(20*6250 +25*4400+65*9500+65*4350)/(6250+4400+9500+4350)$

$=1135250/24500 = 46.35$

On the Scatter plot the existing location are in green while the optimal location is in white

The table that shows the given and obtained data is shown on the fourth uploaded image