4:49? Exam 1 Material Exam1.xlsx 32 (13 points) Answer the following question A

Question

4:49? Exam 1 Material Exam1.xlsx 32 (13 points) Answer the following question A manufacturer of cat towers wishes to locate a super assembly facility to meet their cat tower assembly needs for the next millennium Currently, carpet, cylinders yam and fasteners are purchased in bulk from suppliers in North Haverbrook Ogden, and Springfield in the quantitics shown in the tablc. The super assembly facility would ship to distribution centers located in Scattle, Lubbock, Nashville, and Philadelphia. The locations of all of these cities on an x-y grid, transportation costs on a ton per mile basis, and total tonnage are all contained in the table Formulate and solve a model that will minimize the shipping costs to the super assembly center Where should the new plant be located and what is the total system shipping cost? Note: the where" is not some named location it is an (xy)coordinate) Next Dashboard Calendar To DoNotifications Inbox

Explanation / Answer

Here using the center of gravity model for supply we will locate the location of plant and then using the load distance technique calculate the load distance and cost

Source/Markets

Transportation Cost$/ton Mile (Fn)

Quantity in Tons (Dn)

xn

yn

x coordinate for new plant

y coordinate for new plant

Distance from proposed site

Load distance

Shipping Cost

Supply

A

B

C

D

x=(x1*B1+x2*B2+x3*B3+x4*B4+x5*B5+x6*B6+x7*B7)/(B1+B2+B3+B4+B5+B6+B7)

y=(y1*B1+y2*B2+y3*B3+y4*B4+y5*B5+y6*B6+y7*B7)/(B1+B2+B3+B4+B5+B6+B7)

d=sqrt of(square of (xn-x)+square of (yn-y))

l=B*d

SC=l*A

North Haverbrook

1.1

650

700

1200

549.17

825.00

404.20

262727.6

289000.39

Ogden

1.2

450

250

600

374.34

168451.3

202141.62

Springfield

1.4

400

250

825

299.17

119668

167535.2

Market

Seattle

2.25

300

50

1200

624.34

187300.9

421426.93

Lubbock

2.25

200

450

300

534.28

106856.9

240427.92

Nashville

2.25

500

800

250

627.33

313664.1

705744.24

Philadelphia

2.25

500

950

1100

486.10

243048.2

546858.43

Total Shipping cost

Here using the center of gravity model for supply we will locate the location of plant and then using the load distance technique calculate the load distance and cost

Source/Markets

Transportation Cost$/ton Mile (Fn)

Quantity in Tons (Dn)

xn

yn

x coordinate for new plant

y coordinate for new plant

Distance from proposed site

Load distance

Shipping Cost

Supply

A

B

C

D

x=(x1*B1+x2*B2+x3*B3+x4*B4+x5*B5+x6*B6+x7*B7)/(B1+B2+B3+B4+B5+B6+B7)

y=(y1*B1+y2*B2+y3*B3+y4*B4+y5*B5+y6*B6+y7*B7)/(B1+B2+B3+B4+B5+B6+B7)

d=sqrt of(square of (xn-x)+square of (yn-y))

l=B*d

SC=l*A

North Haverbrook

1.1

650

700

1200

549.17

825.00

404.20

262727.6

289000.39

Ogden

1.2

450

250

600

374.34

168451.3

202141.62

Springfield

1.4

400

250

825

299.17

119668

167535.2

Market

Seattle

2.25

300

50

1200

624.34

187300.9

421426.93

Lubbock

2.25

200

450

300

534.28

106856.9

240427.92

Nashville

2.25

500

800

250

627.33

313664.1

705744.24

Philadelphia

2.25

500

950

1100

486.10

243048.2

546858.43

Total Shipping cost

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