Question

Average maintenance costs are $1.50 per machine-hour at an activity level of 8,000 machine-hours and $1.20 per machine-hour at an activity level of 13,000 machine-hours. assuming that this activity is within the relevant range, total expected maintenance cost for a budgeted activity level of 10,000 machine-hours would be closest to:

Answer 1

Assume that maintenance costs per machine may be modeled by the linear relation
C = a + bx
where
x = machine hours
a, b are constants.

When x=8,000 hours, C=$1.50, therefore
a + 8000b = 1.5            (1)

When x=13,000 hours, C=$1.20, therefore
a + 13000b = 1.2           (2)

Subtract (2) from (1).
a + 8000b - (a + 13000b) = 1.5 - 1.2
-5000b = 0.3
b = -6 x 10⁻⁵
From (1), obtain
a = 1.5 - 8000*(-6 x 10⁻⁵) = 1.98

Therefore
C = 1.98 - 6x10⁻⁵ x

When machine hours is x=10,000, obtain
C = 1.98 - 6x10⁻⁵ * 10000
    = 1.38

Answer: $1.38