30) A manufacturing company is considering two alternative locations for a new facility. The fixed and
variable costs for the two locations are found in the table below. For which volume of business would the
two locations be equally attractive? If the company plans on producing 50,000 units, which location
would be more attractive?
Glen Rose
Mesquite
Fixed Costs
$1,000,000
$1,500,000
Variable Costs ($ per unit)
25
23
Break-even points
Units
Dollars
Option 1 vs. Option 2
250,000
7,250,000
Volume analysis at 50,000 units
Option 1
Option 2
total cost
$2,250,000.00
$2,650,000.00
31) East Texas Seasonings is preparing to build one processing center to serve its four sources of
seasonings. The four source locations are at coordinates shown below. Also, the volume from each source
is provided.
a. Calculate the volume-weighted center of gravity.
b. Calculate the simple center of gravity (all cities weighted equally).
c. Explain why the two calculations differ.
X-coordinate
Y-coordinate
Volume
Athens, Texas
30
40
100
Beaumont, Texas
20
15
400
Carthage, Texas
55
60
150
Denton, Texas
20
70
250
A
B
C
D
Total
Average
Average
Median
32) Location A would result in annual fixed costs of $300,000 and variable costs of $55 per unit. Annual
fixed costs at Location B are $600,000 with variable costs of $32 per unit. Sales volume is estimated to be
30,000 units per year. Which location has the lower cost at this volume? How large is its cost advantage?
At what volume are the two facilities equal in cost?
33) Using the factor ratings shown below, determine which location alternative should be chosen on the
basis of maximum composite score.
Location
Factor
Weight
A
B
C
Easy access
0.15
86
72
90
Parking facilities
0.20
72
77
91
Display area
0.18
86
90
90
Shopper (walking) traffic
0.21
94
86
80
Neighborhood wealth
0.16
99
89
81
Neighborhood safety
0.10
96
85
75
34) A manager has received an analysis of several cities being considered for a new order fulfillment
center (warehouse) for Shop at Home Network. The scores (scale is 10 points = best) are contained in the
table below.
a. If the manager weights the factors equally, how would the locations be ranked?
b. If transportation costs and operating costs are given weights that are double the weights of the others,
should the locations be ranked differently?
Location
Factor
W
X
Z
Business services
7
9
4
Community services
5
7
7
Real estate cost
7
3
6
Construction costs
8
6
5
Operating costs
5
4
6
Business taxes
6
9
4
Transportation costs
8
6
8
Factor
Business services
1
9
5
4
Community services
1
7
6
7
Real estate cost
Construction costs
1
6
6
5
Operating costs
Business taxes
1
9
6
4
Transportation costs
1
6
7
8
Total
Weighted average
X
Y
Z
Business services
Community services
Real estate cost
1
3
8
6
Construction costs
Operating costs
2
4
7
6
Business taxes
Transportation costs
2
6
7
8
Total
9
Weighted sum
Weighted average
6
6
35) A telecommunications firm is planning to lay fiber optic cable from several community college
distance learning sites to a central studio, in such a way that the miles of cable are minimized. Some
locations require more than one set of cables (these are the loads). Where should the studio be located to
accomplish the objective?
College
Map Coordinate (x, y)
Load
A
(2,10)
3
B
(6,8)
2
C
(4,9)
4
D
(9,5)
1
E
(8,1)
3
F
(3,2)
2
G
(2,6)
1
3
2
2
6
8
4
4
9
1
9
5
3
8
1
2
3
2
1
2
6
36) The owner of a millwork shop is considering three alternative locations for a new plant for building
embossed-and-clad steel exterior doors for residences. Fixed and variable costs follow. Since the plant
ships nationwide, revenue is assumed the same regardless of plant location. Identify the range over
which each location is best.
Location
Costs
A
B
C
Fixed
$700,000
$1,000,000
$1,1000,000
Variable
$28
$18
$20
Break-even points
Location A vs. Location B
$1,540,000
Location A vs. Location C
Location B vs. Location C
$100,000
37) A manufacturing firm is considering three potential locations for a new parts manufacturing facility.
A consulting firm has assessed three sites based on the four factors supplied by management as critical to
the location’s success. Given the management-supplied factor weights and the consultant team scores,
which location should be selected? Scores are based on 50 = best.
Location
Factor
A
B
C
Labor Climate
35
45
20
Taxes
30
40
40
Utilities
25
20
45
Wages
10
25
25
Factor
Labor Climate
10
35
45
20
Taxes
30
30
40
40
Utilities
20
25
20
45
Wages
40
10
25
25
Total
Weighted sum
Weighted average
38) Environmental Glass Products, Inc. wants to build a new centralized facility to receive household,
commercial, and industrial glass for recycling. This center will be supplied by trucks coming from four
“collection points,” where recyclable glass is dropped off by individuals and businesses. The volume and
the map coordinates for the four collection centers are shown below. Where should the collection center
be located?
Collection point
Load
(X,Y) Coordinates
A
9,000
(4,8)
B
4,000
(7,2)
C
2,000
(4,1)
D
5,000
(7,3)
9,000
2,000
5,000
39) A manufacturer of stamped metal auto parts has four parts factories in one city at the location
coordinates shown below. Each coordinate unit represents a city block (roughly 100 meters). The yearly
demand at each factory is also given.
Factories
Demand
X-Coord.
Y-Coord.
Rayburn Industrial Park
19,000
20
130
Port of Zavalla
3,000
60
40
Henderson Mfg. Center
5,000
70
100
Wax Mills Site
6,000
90
30
Management has decided to build a new sheet metal mill, to supply these factories, at a location central to
these plants. What should be the map coordinates of the new plant?
Rayburn
Zavalla
Henderson
Wax MIlls
Total
Average
Average
40) A small producer of music boxes wants to move to a larger facility. Two alternative facilities have
been found. Site 1 has a fixed cost of $500,000 per year, with a variable cost of $25 per unit. Site 2 has a
fixed cost of $800,000 per year, but a variable cost of $22 per unit.
a. Write out the equation for total cost for each site.
b. At what volume of output would the two locations have the same total cost?
c. For what range of output would Site 1 be superior?
d. For what range of output would Site 2 be superior?
41) A small manufacturer is considering several locations for a new facility. They have identified four
factors that they consider to be important for their location decision. They have decided to assign scores
to the four factors, with a higher score indicating a more favorable location. Use the information in the
following table to perform a factor rating to select the best location.
Location A
Location B
Location C
Wages
30
75
90
Labor Climate
40
70
40
Taxes
80
40
90
Utilities
75
60
10
Wages
40
30
75
90
Labor Climate
30
40
70
40
Taxes
15
80
40
90
Utilities
15
75
60
10
Total
Weighted sum
Weighted average
42) A contractor for the military is looking for a new location for a supply depot. The depot will supply
four bases whose tonnage (demand) and map coordinates are shown below. If management wants the
depot to have a central location, what should be its map coordinates?
Bases
(X,Y) Coordinates
Tonnage
Fort Able
(40,110)
30,000
Base Baker
(70, 50)
60,000
Camp Charlie
(90, 20)
35,000
Camp Delta
(70, 80)
75,000
Bases
Fort Able
Base Baker
Camp Charlie
Camp Delta
Sum
Weighted Average