At the high and low levels of activity during the month, direct labor hours are 90,000 and 40,000, respectively. The related costs are $165,000 and $100,000. What are the fixed and variable costs at any level of activity?

The fixed cost at any level of activity is $48,000 while the variable cost per unit at any level of activity is $1.30

Explanation:

The total cost is a function of the fixed and variable cost. Whilst the fixed cost does not change at a certain range of activities level, the variable cost changes as the level of activities (units produced or sold).

Using the high and low levels of activities given, let the variable cost per unit be v and the fixed cost F

for the high level,

F + 90,000v = 165,000

For the low level

F + 40,000v = 100,00

Solving both equations simultaneously,

50,000v = 65,000

v = $1.30

F + 40,000 ($1.30) = 100,000

F = 100,000 - 52,000

F = $48,000