The Fairport Machine Shop wants to develop a cost estimating equation for its monthly cost of
electricity. It has the following data:
Cost of Electricity (Y)
$13,000
$15,000
$17,000
$14,500
Direct Labor-Hours (X)
1,500
1,700
2,000
1,600
What would be the best equation using the high-low method?
I think the answer is Y = $1,000 + $8X but when I went to confirm the equation by plugging in x and y values, the equation didn't hold true. Please help.
To use the high-low method to develop a cost estimating equation, we need to find the variable cost per unit and the fixed cost.
Let's start by finding the variable cost per unit using the high (the highest value pair) and low (the lowest value pair) data points:
High data point:
Cost of Electricity (Y) = $17,000
Direct Labor-Hours (X) = 2,000
Low data point:
Cost of Electricity (Y) = $13,000
Direct Labor-Hours (X) = 1,500
To find the variable cost per unit, you need to find the change in the cost of electricity (ΔY) divided by the corresponding change in direct labor-hours (ΔX):
ΔY = $17,000 - $13,000 = $4,000
ΔX = 2,000 - 1,500 = 500
Variable cost per unit = ΔY / ΔX = $4,000 / 500 = $8
Next, we can find the fixed cost. We'll use either the high or low data points and the variable cost per unit:
Using the high data point:
Cost of Electricity (Y) = $17,000
Direct Labor-Hours (X) = 2,000
Variable cost per unit = $8
Fixed cost = Y - (variable cost per unit * X)
Fixed cost = $17,000 - ($8 * 2,000)
Fixed cost = $17,000 - $16,000
Fixed cost = $1,000
So, the estimated cost equation using the high-low method would be:
Y = $1,000 + $8X
Now, let's verify it by plugging in the values from the given data:
Plugging in the high data point:
Y = $1,000 + $8 * 2,000
Y = $1,000 + $16,000
Y = $17,000
Plugging in the low data point:
Y = $1,000 + $8 * 1,500
Y = $1,000 + $12,000
Y = $13,000
As we can see, the equation holds true for both the high and low data points. There might have been some calculation error when you checked it earlier. Please try again using the correct equation: Y = $1,000 + $8X.