Question

Question 1

The operations manager for Fine Foods Distribution has narrowed the search for a new facility to seven communities. Fixed costs (land, buildings and equipment) and variable costs (labour, materials etc) are shown below.

Project Parameters

Community	Fixed Costs ($millions)	Variable Costs ($)
Aurora	$1,600	17
Boulder	2,000	12
Cranbrook	1,500	16
Deerfield	3,000	10
Essex	1,800	15
Farber	1,200	15
Grafton	1,700	14

1. Which of the communities can be eliminated from further consideration because they are dominated (both variable and fixed costs are higher) by another community?
2. Plot the total cost curves for all remaining communities on a single graph. Identify on the graph the approximate range over which each community provides the lowest cost.
3. Using locational break-even analysis, calculate the break-even quantities to determine the range over which each community provides the lowest cost.

Answer 1

Community	FC	VC
Aurora	1600	17
Boulder	2000	12
Cranbrook	1500	16
Deerfield	3000	10
Essex	1800	15
Farber	1200	15
Grafton	1700	14

a. Essex that has FC of 1800 and VC of 15 is higher than Grafton for both. Hence can be eliminated
Also, Aurora with FC of 1600 and VC of 17 is higher than Cranbrook for both. Hence can be eliminated
Further, Cranbook can be eliminated as FC of 1500 and VC of 16 is higher than Farber

b. Total cost for remaining communities are plotted below

Different graphs have different slopes and will intersect at different points
Farber and Grafton will intersect at X = 500
Farber and Boulder will intersect at X = 267
Farber and Deerfield will intersect at X = 360
Grafton and Boulder will intersect at X = 150
Grafton and Deerfield will intersect at X = 325
Boulder and Deerfield will intersect at X = 500
So the earliest cutoff point is X=150.
Till X=150 none of the graphs intersect hence the range for lowest cost for each
community is from X = 0 to 150

c. Using locational break-even analysis, calculate the break-even quantities to
determine the range over which each community provides the lowest cost.
For Farber, Fixed cost = qty x VC
1200 = 15x i.e. x = 80
For Grafton, 1700 = 14x
i.e. x = 121.43 ~ 122
For Boulder, 2000 = 12x
i.e. x = 166.67 ~167
For Deerfield, 3000 = 10x
i.e. x = 300
So the range of breakeven quantities are 80 to 300
However, beyond X = 150, grafton and boulder intersect as seen in part b above
So the range of breakeven quantities over which each community provides lowest cost is 80 to 150