A manufacturing firm is considering two locations for a plant to produce a new product. the two locations have fixed and variable costs as follows: locationfc (annual) vc (per unit) atlanta$80,000 $20 phoenix$140,000 $16 at what annual output would the company be indifferent between the two locations?

Answer: The answer is 15,000 units per annum

Explanation:

for Atlanta:

Fixed cost = $80000

Variable cost = $20 per unit

For Phoenix:

Fixed cost = $140000

Variable cost = $16

Total cost = VC + FC

Since we do not know the number of units, let us represent it with 'n'

For Atlanta:

Total cost = $80000 + ($20 x n)

For Phoenix:

Total cost = $140000 + ($16 X n)

To calculate the indifference between locations, total cost of Atlanta and Phoenix must be equal, therefore we have:

80000 + 20n = 140000 + 16n

20n - 16n = 140000 - 80000

4n = 60000

Divide both sides by 4, we have:

n = 15,000 units per annum

Answer: 15,000 units per annum

Explanation;

for Atlanta, FC = $80000

VC = $20 per unit

For Phoenix, FC = $140000

VC = $16

Total cost = VC + FC

Atlanta TC = $80000 + ($20 x n)

Phoenix TC = $140000 + ($16 X n)

Where n = number of units

for indifference between locations, total cost must be equal,

Therefore,

80000 + 20n = 140000 + 16n

20n - 16n = 140000 - 80000

4n = 60000

n = 1500 units per annum