The algebraic formula for a mixed cost is

**y**=

**a**+

**bx**, where

**y**is the total cost,

**a**is the fixed cost per period,

**b**is the variable rate per unit of activity, and

**x**is the number of units of activity. For the annual expense of operating an automobile, the fixed cost,

**a**, might be $5,000 per year; the variable rate,

**b**, could be $0.20; and the number of units of activity,

**x**, might be 15,000 miles per year. With these hypothetical assumptions, the annual expense,

**y**, would be $8,000. If

**x**were 10,000 miles, the annual expense

**y**would be $7,000.

To gain insight on the behavior of a mixed cost, it is helpful to graph the cost: For each observation, indicate a point on the graph where the total mixed cost amount aligns with the amounts on y-axis and also aligns with the activity amounts on the x-axis. To compute the best fitting line through the graphed data, you could use a mathematical tool known as regression analysis. This will calculate the fixed expenses,

**a**, and the variable rate,

**b**, based on the historical data that is utilized.

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