A manufacturing firm is considering two locations for a plant to produce a new p

Question

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: Site Fixed Cost (Annual) Variable Cost (per unit) A $100,000 $10 B $120,000 $8 C $150,000 $7 a) For what quantity would there be indifferent between selecting site A or site B? b) For what range of output would you prefer site C? c) Which site would you prefer for a quantity of 20,000 units per year? What would be your total cost? Please provide formulas with answers for rating!

Explanation / Answer

Part a:
let the unit = x
so, we have ,
( $100,000 + 10*x) = ( 120,000 + 8 * x )
2 * x = 20000
x = 10000
so, for 10000 units, there be indifferent between selecting site A or site B.

Part b:
for this we have to find the break even points for A and C, B and C/
it is:
A and C::
( $100,000 + 10*x) = ( 150,000 + 7 * x )
x = 16666 units

B and C::
( 120,000 + 8 * x ) = ( 150,000 + 7 * x )
x = 30000 units,
so, the range is:
x>30000 units

Part c:
for 20000 units,
cost at A:300000
B:280000
C:290000

We will use Site B, total cost = 280000 $

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