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22 June, 08:30

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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  1. 22 June, 09:08
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    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
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