chap008hwsolutions.doc

Chapter 08 - Location Planning and Analysis

Solutions1. Profit = (Rev/unit – VC/unit)Q – FC

Omaha: ($185/unit – $36/unit)8,000 units – $1,200,000 = –$8,000

K.C.: ($185/unit – $47/unit)12,000 units – $1,400,000 = $256,000

2. Location

A B CRev/unit $2.65 $2.65 $2.65

VC/unit 1.76 1.76 1.76

FC $5,000 $5,500 $5,800

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a. Q =specified profit + FC A B CRev/unit – VC/unit = 16,854 17,416 17,753

b. Profit = (Rev/unit – VC/unit)Q – FC = $13,690 $14,080 $14,670

3. A BFC $800,000 $920,000

VC/unit $14,000 $13,000

Rev/unit $17,000 $17,000

a. TC = VC/unit x Q + FC

[A] [B]

$14,000Q + $800,000 = $13,000Q + $920,000

Solving, Q = 120 units

b. A: 0 to 119

B: 121 or more

4. A B CFC/year $250,000 $50,000

VC/unit 500 2,500 1,000

a.

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A (new location)

C (expansion)

B (sub-contract)

33.3 100 200 300 400

500

400

300

200

100

0

TC($000)

B C A

[250]

[50]

No. of Boats/yr.


b. C (from graph)

c. Subcontracting prices are probably more precise, subcontracting provides another source of supply. Expansion would allow more control and flexibility.

5. A B C

FC $254,000 $25,000 $120,000

VC/unit 500 2,500 1,000

TC = VC/unit x Q + FC

A: $500(150) + $254,000 = $329,000

B: $2,500(150) + $25,000 = $400,000

C: $1,000(150) + $120,000 = $270,000*

6. Memphis Biloxi Birmingham

Lease, equipment $40,000 $60,000 $100,000

Transportation 50,000 60,000 25,000

“Fixed” Costs $90,000 $120,000 $125,000

VC/unit $8 $4 $5

Memphis Biloxi Birming-ham

TC = VC/unit x Q + FC: $170,000 $160,000 $175,000

7. City Outside

FC/month $7,000 $4,700

VC/unit $30 $40

Rev/unit $90 $90

Profit = (rev/unit – VC/unit) – FC

City Outside

a. P200 $5,000 $5,300*

P300 11,000* 10,300

b. ($90 – $30)Q – $7,000 = ($90 – $40)Q – 4,700

Solving, Q = 230 cars

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8. Factor Local bank Steel mill Food warehouse Public school1. Convenience for

customers H L M–H M–H2. Attractiveness of

building H L M M–H3. Nearness to raw

materials L H L M4. Large amounts

of power L H L L5. Pollution

controls L H L L6. Labor cost and

availability L M L L7. Transportation

costs L M–H M–H M8. Construction

costs M H M M–H

9. Factor Wt. A B C1. Conv. access .15 .15(80) = 12.00 .15(70) = 10.50 .15(60) = 9.0

2. Parking .20 .20(72) = 14.40 .20(76) = 15.20 .20(92) = 18.4

3. Display area .18 .18(88) = 15.84 .18(90) = 16.20 .18(90) = 16.2

4. Shopper traffic .27 .27(94) = 25.38 .27(86) = 23.22 .27(80) = 21.6

5. Operating costs .10 .10(98) = 9.80 .10(90) = 9.00 .10(82) = 8.2

6. Neighborhood .10 .10(96) = 9.60 .10(85) = 8.50 .10(75) = 7.5

1.00 87.02 82.62 80.9

On the basis of composite score, A seems the best.

10. Factor Wt. East #1 East #2 West

1. Initial Cost 8 8(100) = 800 8(150) = 1200 8(140) =1120

2. Traffic 10 10(40) = 400 10(40) = 400 10(30) = 300

3. Maintenance 6 6(20) = 120 6(25) = 150 6(18) = 108

4. Dock space 6 6(25) = 150 6(10) = 60 6(12) = 72

5. Neighborhood 4 4(12) = 48 4(8) = 32 4(15) = 60

1518 1842 1660

On the basis of composite score, .East # 2 is best.

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Location (a) Location (b)11. Factor A B C Weight A B C

1. Business Services 9 5 5 2/9 18/9 10/9 10/9

2. Community Services 7 6 7 1/9 7/9 6/9 7/9

3. Real Estate Cost 3 8 7 1/9 3/9 8/9 7/9

4. Construction Costs 5 6 5 2/9 10/9 12/9 10/9

5. Cost of Living 4 7 8 1/9 4/9 7/9 8/9

6. Taxes 5 5 5 1/9 5/9 5/9 4/9

7. Transportation 6 7 8 1/9 6 /9 7 /9 8 /9

Total 39 44 45 1.0 53/9 55/9 54/9

Each factor has a weight of 1/7.

a. Composite Scores 39 44 457 7 7

B or C is the best and A is least desirable.

b. Business Services and Construction Costs both have a weight of 2/9; the other factors each have a weight of 1/9.

5 x + 2 x + 2 x = 1 x = 1/9

c. Composite Scores A B C

53/9 55/9 54/9B is the best followed by C and then A.

12.Location

x y

A 3 7

B 8 2

C 4 6

D 4 1

E 6 4

Totals 25 20

(=xi = 25 = 5.0 (=

yi = 20 = 4.0n 5 n 5

Hence, the center of gravity is at (5,4) and therefore the optimal location.

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13. Location x y 0

A 5 7 15

B 6 9 20

C 3 9 25

D 9 4 30

Totals 23 29 90

(=xiQi

=5(15) + 6(20) + 3(25) + 9(30)

=540

= 6.0Qi 90 90

(=xiQi

=7(15) + 9(20) + 9(25) + 4(30)

=630

= 7.0Qi 90 90

The center of gravity and optimal location is (6,7).

14. Location Volume inx y Tons Per Day

10 5 26

4 1 9

4 7 25

2 6 30

8 7 40

28 26 130

(= xiQi=

10(26) + 4(9) + 4 (25) + 2(30) + 8(40)

Qi 130

(= 776 = 5.97

130(= yiQi

=5(26) + 1(9) + 7(25) + 6(30) + 7(40)

Qi 130

(= 774 = 5.95

130

Hence, the center of gravity and optimal location.

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15.

Destinationx, y

Coordinates Quantity xQ yQD1D2D3D4D5

1,22,43,14,25,3

900 300 700 6001,200

900 6002,1002,4006,000

1,8001,200 7001,2003,600

3,700 12,000 8,500

x = 12,000 3,700

= 3.24

y = 8,500 3,700

= 2.30

Plotting the coordinates on the graph given in the problem reveals that L2 is closest to the center of gravity.

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