Highland Rose Ltd is attempting to develop the cost function for repair costs. The following past data are available: $$\begin{array} { c c }
\underline{\text { Machine Hours} } & \underline{\text { Repair Costs }} \
4,800 & \$ 6,385 \
3,400 & 4,585 \
4,000 & 5,285 \
5,900 & 7,085
\end{array}$$ Using the high-low method, what is the estimated repair cost for 4,500 machine hours?
A) $5,785
B) $5,585
C) $5,985
D) $5,685

Question

Highland Rose Ltd is attempting to develop the cost function for repair costs. The following past data are available: $$\begin{array} { c c } 
\underline{\text { Machine Hours} } & \underline{\text { Repair Costs }} \
 4,800 & \$ 6,385 \
3,400 & 4,585 \
4,000 & 5,285 \
5,900 & 7,085
\end{array}$$ Using the high-low method, what is the estimated repair cost for 4,500 machine hours?
A) $5,785
B) $5,585
C) $5,985
D) $5,685

Quizplus · Accepted Answer

First, identify the highest and lowest activity levels. The highest is 5,900 hours with costs of $7,085, and the lowest is 3,400 hours with costs of $4,585. The variable cost per machine hour is calculated as: $$ \frac{\$7,085 - \$4,585}{5,900 - 3,400} = \frac{\$2,500}{2,500} = \$1 $$ per machine hour. The fixed cost is found by subtracting the total variable cost at either level from the total cost at that level. Using the high level: $$ \$7,085 - (5,900 \times \$1) = \$1,185 $$ The total cost function is: $$ \text{Total Cost} = \$1,185 + \$1 \times \text{Machine Hours} $$ For 4,500 machine hours, the estimated repair cost is: $$ \$1,185 + \$1 \times 4,500 = \$5,685 $$

Highland Rose Ltd Is Attempting to Develop the Cost Function