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:

Question

Dangelo Petty

Mathematics

2 December, 18:32

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:

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Haylee Perkins · 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