Consider a manufacturing facility where monthly Plant Utility Overhead ($Y$) depends on two validated cost drivers derived via Multiple Linear Regression (MLR): Machine Running Hours ($X_1$) and Direct Kilowatt-Hours Consumed ($X_2$).
Established Cost Function
From historical facility data, the MLR model produced the following validated cost equation:
$$Y = \$5,000 + \$12.00(X_1) + \$0.15(X_2)$$
- Fixed Facility Overhead ($a$): $\$5,000$ per month (facility maintenance, baseline lighting, HVAC).
- Machine Hours Driver Rate ($b_1$): $\$12.00$ per machine hour (wear-and-tear utilities, machine lubrication).
- Energy Consumption Driver Rate ($b_2$): $\$0.15$ per kWh (direct process power usage).
Monthly Production and Operational Usage
During the month, the plant produced two product lines with the following driver consumption:
| Operational Parameter | Product Line A | Product Line B | Total Facility |
| Units Produced | 5,000 units | 1,000 units | 6,000 units |
| Machine Running Hours ($X_1$) | 800 hours | 1,200 hours | 2,000 hours |
| Energy Consumed ($X_2$) | 40,000 kWh | 60,000 kWh | 100,000 kWh |
Step 1: Calculate Total Monthly Utility Overhead
Using the MLR equation across total facility metrics:
$$Y_{\text{total}} = \$5,000 + \$12.00(2,000) + \$0.15(100,000)$$
$$Y_{\text{total}} = \$5,000 + \$24,000 + \$15,000 = \mathbf{\$44,000}$$
Step 2: Allocate Costs to Individual Product Lines
To assign the total $\$44,000$ utility overhead, allocate both variable driver costs directly to each product based on usage, and distribute the $\$5,000$ fixed baseline overhead proportionally based on total machine hours.
Proportional Fixed Overhead Allocation
$$\text{Fixed Allocation Share for Product A} = \frac{800}{2,000} = 40\% \implies 40\% \times \$5,000 = \$2,000$$
$$\text{Fixed Allocation Share for Product B} = \frac{1,200}{2,000} = 60\% \implies 60\% \times \$5,000 = \$3,000$$
Detailed Overhead Allocation Breakdown
| Cost Component | Product Line A | Product Line B | Total Overhead |
| Fixed Facility Base ($a$) | $\$2,000$ | $\$3,000$ | $\$5,000$ |
| Machine Hours Cost ($\$12 \times X_1$) | $800 \times \$12 = \$9,600$ | $1,200 \times \$12 = \$14,400$ | $\$24,000$ |
| Power Consumption Cost ($\$0.15 \times X_2$) | $40,000 \times \$0.15 = \$6,000$ | $60,000 \times \$0.15 = \$9,000$ | $\$15,000$ |
| Total Allocated Overhead | $\$17,600$ | $\$26,400$ | $\$44,000$ |
Step 3: Compute Unit Utility Overhead Rates
Divide each product line's total allocated utility cost by its production volume:
- Product Line A (High-Volume Standard Item):$$\text{Unit Overhead Cost} = \frac{\$17,600}{5,000 \text{ units}} = \mathbf{\$3.52 \text{ per unit}}$$
- Product Line B (Low-Volume Heavy Item):$$\text{Unit Overhead Cost} = \frac{\$26,400}{1,000 \text{ units}} = \mathbf{\$26.40 \text{ per unit}}$$
Key Insight
Product B uses 60% of both machine hours and power, despite representing only 16.7% of total physical unit output. Using the MLR allocation model accurately charges Product B $26.40 per unit compared to $3.52 per unit for Product A, reflecting true resource consumption and preventing cost distortion.