Problem 8-3 A small producer of machine tools wants to move to a larger building
ID: 3120158 • Letter: P
Question
Problem 8-3
A small producer of machine tools wants to move to a larger building, and has identified two alternatives. Location A has annual fixed costs of $200,000 and variable costs of $12,000 per unit; location B has annual fixed costs of $400,000 and variable costs of $10,000 per unit. The finished items sell for $15,000 each.
For what range of output would location A be superior? (Enter your answer as a whole number. Do not include the indifference point in your answer.)
For what range would B be superior? (Enter your answer as a whole number. Do not include the indifference point in your answer.)
A small producer of machine tools wants to move to a larger building, and has identified two alternatives. Location A has annual fixed costs of $200,000 and variable costs of $12,000 per unit; location B has annual fixed costs of $400,000 and variable costs of $10,000 per unit. The finished items sell for $15,000 each.
Explanation / Answer
a) For same total cost, let toal numbe rof units = x
200000+12000x = 400000+10000x
2000x = 200000
x = 100 units
b) 1. For location A to be superior profit from A should be greater than B
So,
15000x - (200000+12000x) > 15000x - (400000+10000x)
or
- (200000+12000x) > - (400000+10000x)
Multiplying by 1 would change the inequality sign
(200000+12000x) < (400000+10000x)
2000x < 200000
x < 100
So, From 0 to 99 units A location would be superior
For B to be superior, profit from B>profit from A
15000x - (400000+10000x) > 15000x - (200000+12000x)
- (400000+10000x) > - (200000+12000x)
(400000+10000x) < (200000+12000x)
200000 < 2000x
x > 100