Question

Susan Bromley, operations manager at Enviro-Tech, Inc., has collected data concerning three new plant locations. The fixed and variable costs for these three locations are as follows:

Location	Fixed Cost per Year	Variable Cost per Unit
1	$500, 000	$1,000
2	$1,700,000	$200
3	$1,100,000	$500

1. What is the Total Cost (TC) equation for each alternative location for any capacity size Q units?
2. Calculate the break-even quantity for locations 1 and 2, 1 and 3, and 2 and 3.
3. Plot the total cost curves for the three potential locations on a graph. Using this graph, identify the range in volume over which each location would be best.

Answer 1

a)

Total Cost Equations for each alternative location are following:

TC = Fixed cost + Variable cost per unit * Q

TC1 = 500000+1000Q

TC2 = 1700000+200Q

TC3 = 1100000+500Q

b)

Break-even quantity for locations 1 and 2 = (Fixed cost of location 2 - Fixed cost of location 1) / (Variable cost of location 1 - Variable cost of location 2)

= (1700000-500000)/(1000-200)

= 1500 units

Break-even quantity for locations 1 and 3 = (Fixed cost of location 3 - Fixed cost of location 1) / (Variable cost of location 1 - Variable cost of location 3)

= (1100000-500000)/(1000-500)

= 1200 units

Break-even quantity for locations 2 and 3 = (Fixed cost of location 3 - Fixed cost of location 2) / (Variable cost of location 2 - Variable cost of location 3)

= (1100000-1700000)/(200-500)

= 2000 units

c)

Create the Total Cost table for different quantities as below:

Location	1	2	3
Fixed Cost (FC)	500,000	1,700,000	1,100,000
Variable Cost (VC)	1,000	200	500
	Total Cost = FC + Q * VC
Quantity (Q)	1	2	3
0	500,000	1,700,000	1,100,000
1,200	1,700,000	1,940,000	1,700,000
1,500	2,000,000	2,000,000	1,850,000
2,000	2,500,000	2,100,000	2,100,000
3,000	3,500,000	2,300,000	2,600,000

Using the data in above table, Total Cost curves for the three potential locations are plotted as below:

Range in volume over which each location is best is following:

Alternative	Most economical Quantity (Q) range
Location 1	0	< Q ≤	1,200
Location 3	1,200	< Q ≤	2,000
Location 2	2,000	< Q <	Inifnity