A company needs to locate three departments X, Y, and Z in the three areas I, II, and III of a new facility. They want to minimize interdepartmental transportation costs, which are expected to be $.50 per load meter moved. An analyst has prepared the following flow and distance matrices: Distances meters Flows Loads per week
From / To I II III From / To X Y Z
I - 10 20 X - 0 80
II - - 10 Y 30 - 150
III - Z 100 130 -
If the company were to locate departments X, Y, and Z in areas 1, 2, and 3, respectively, what would be the total distance (in meters) loads would be moved each week?
A. 3,100
B. 3,600
C. 6,200
D. 7,200
E. 8,200

A. 3,100

the total distance (in meters) loads that would be moved each week is  3,100

Explanation:

First we arrange the workflow of the departments in descending order while the distance will be in ascending order.

TRIPS                                  DISTANCE(metres)

1 -11                                       10

11 - 111                                   10

1 - 111                                     20

DEPARTMENTAL PAIR       WORKFLOW

Y-Z                                         150

Z-Y                                         130  

Z-X                                         100

X-Z                                         80

Y-X                                         30  

Given that question provided to allocate departments X, Y, and Z in areas 1, 2, and 3 respectively.

So, having that in mind, allocate the distance for each suitable departmental pair;

DEPARTMENTAL PAIR     WORKFLOW     DISTANCE    TOTAL DISTANCE    

                                                                                               (meter loads)

Y-Z                                         150                        10                      1500

Z-Y                                         130                         -

Z-X                                         100                        10                      1000

X-Z                                         80                           -

Y-X                                         30                         20                       600

                                                                                                       3100

Therefore the total distance (in meters) loads that would be moved each week is  3,100                          

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