Finding Total Utility Cost

[unreal030]

I am having trouble with this. I don't really know where to start/what equation to use.

Utility costs at Service, Inc. are a mixture of fixed and variable components. Records indicate that utility costs are an average of $0.40 per hour at an activity level of 9,000 machine hours and $0.25 per hour at an activity level of 18,000 machine hours. Assuming that this activity is within the relevant range, what is the expected total utility cost if the company works 13,000 machine hours?

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So I am not sure if this helps with the problem at all but I figured out how much it was total for each of those.

.40/hour at 9,000 hours = .40x9,000=$3,600 total utility cost

.25/hour at 18,000 hours=.25x18,000=$4,500 total utility cost

18,000 hours is exactly double 9,000 so....there is a variable increase of 1.25 cents per 1,000 hour?

I am completely lost as you can see. Please help with this!

 

[stapel]

Without specific information about the type of model you're supposed to find, or at least assume (linear? quadratic? something else?), I don't know how one could arrive at "the" answer. Sorry!

Eliz.

 

[mmm4444bot]

If you had been told that this corporation's total utility cost is a linear function of their activity level, then you could use the algebra of lines to determine the requested average.

(9000, 0.4) would be the coordinates of a point on the line which is the graph of this linear function.

(18000, 0.25) would be the coordinates of another point on the line.

You would then need to find the y-coordinate of the point on the line where x equals 13000.

You could first use the Slope formula to find the line's slope.

You could then use the Point-Slope formula to write the line's equation.

You could finish by substituting 13000 for x into the line's equation, and solving for y.