Location Problems
1. Hugh Leach Corp., a producer of machine tools, wants to move to a
larger site. Two alternative locations have been identified: Bonham and
McKinsey. Bonham would have fixed cost of $800,000 per year and
variable costs of $14,000 per standard unit produced. McKinsey would
have fixed costs of $920,000 and variable costs of $13,000 per standard
unit. The finished item sells at $29,000 each.
Required:
1. At what volume of output would both locations have the same profit?
2. For what range of output would Bonham be superior
3. For what range of output would McKinsey be superior
4. What is the relevance of breakeven points for these cities
1. ProfitBonham = – 800,000 + (29000 – 14000)X
= – 800,000 + 15000X
ProfitMcKinney = – 920,000 + (29000 – 13000)X
= – 920,000 + 16000X
Crossover is where ProfitBonham = ProfitMcKinney;
or – 800,000 + 15000X = – 920,000 + 16000X
Crossover is at 120 units.
2,3 McKinney is preferable beyond 120 units, Bonham below 120 units.
4 Bonham has break even at about 53 units; McKinney about 58, so both are beyond
break even at the crossover.
2. A company that produces pleasure boats has decided to expand one of its
current lines. Current facilities are insufficient to handle the increased
workload, so the company is considering three alternatives: A (New
Location), B (Subcontract), and C (Expand existing facilities).
Alternative A would involve substantial fixed cost but relatively low
variable cost: fixed costs would be $250,000 per year and variable costs
would $500 per boat. Subcontracting would involve a cost per boat of
$2,500, and Expansion would require an annual fixed cost of $50,000 and
a variable cost $1,000 per boat.
Required:
a. Plot the data mentioned to find the range of output for each
alternative that would yield the lowest cost.
b. Which alternative would yield the lowest total cost of expected
volume of 150 boats.
c. What other factors might be included in the choice between
expansion and subcontracting?
A B C
FC/year $250,000 $50,000
VC/unit 500 2,500 1,000
a. 500
400 A (new location)
TC
($000)
300
[250] C (expansion)
200 B (sub-
contract)
100
[50]
0 33.3 100 200 300 400
B C A
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.
3. The fixed and variable costs for three potential plant sites for a new factory are
as follows:
Site Fixed Cost per year Variable cost per unit
1 $500 $11
2 1,000 7
3 1,700 4
Required:
1. Draw a graph indicating over which range is every location optimal
2. For a production of 200 units, which location is optimal?
The following figure indicates the volume range for which each site is optimal.
Site 1 is optimal for production less than or equal to 125 units.
Site 2 is optimal for production between 125 and 233 units.
Site 3 is optimal for production above 233 units.
For 200 units, site 2 is optimal.
4. Determine the center of gravity location for the destinations and shipping
quantities shown below. Interpret your results.
The following data shows the center of gravity for this company.
5. Two locations are under consideration for building a condominium. (A
condominium is a building in which each apartment is owned by the
resident, rather than rented.) One location is in suburb A of a large
Eastern city, and the other is in suburb B. The marketing manager has
identified the following factors which bear upon the location decision and
their relative weights.
Factor Desirable Status Weight
1. Proximity to public transportation Should be close .20
2. Space for a parking lot Should be large .40
3. Property taxes Should be low .25
4. Electricity rates Should be low .15
Each factor will be rated on a scale of 1 = unsatisfactory to 10 = outstanding. Research has
revealed the following information about each location, and the marketing manager has rated
each factor at each location.
Location Rating
Factor A B A B
1. Public transportation 1 block 6 blocks 9 2
2. Parking lot 1 acre 3 acres 3 7
3. Property taxes $600/year $800/year 6 4
4. Electric rates $.09/kwh. $.06/kwh. 5 8
Required:
a. Determine the composite score for each location.
b. Where should the condominium be built? Why?
Score Weighted score
Factor Weight A B A B
1. Public Transportation .20 9 2 1.80 0.40
2. Parking lot .40 3 7 1.20 2.80
3. Property taxes .25 6 4 1.50 1.00
4. Electricity rates .15 5 8 0.75 1.20
5.25 5.40
The condominium should be built in suburb B, since it has the higher composite score.
