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Difficulty: HardWages, Salaries, and Commissions

A manufacturing employee earns a base wage of $15.00\$15.00 per hour for a standard 40-hour workweek, with time-and-a-half pay for any additional hours worked. In addition to hourly wages, the employee earns a piece-rate bonus for every unit produced that exceeds a weekly quota of 100 units. Last week, the employee worked 48 hours, produced 180 units, and earned a total gross pay of $1,060.00\$1,060.00. What is the piece-rate bonus paid for each unit produced over the quota?

  1. A
    $2.80\$2.80
  2. $3.50\$3.50Answer
  3. C
    $4.25\$4.25
  4. D
    $7.00\$7.00

Answer

The piece-rate bonus is $3.50\$3.50 per unit.
The correct piece-rate is found by first isolating the hourly wages. The employee earned $600.00\$600.00 for 40 regular hours and $180.00\$180.00 for 8 overtime hours (at $22.50\$22.50/hr), totaling $780.00\$780.00. Subtracting this from the $1,060.00\$1,060.00 gross pay leaves a $280.00\$280.00 bonus pool. Since the employee produced 80 units above the 100-unit quota, the rate per excess unit is $280.00÷80=$3.50\$280.00 \div 80 = \$3.50.

Step-by-Step Solution

1
Calculate the total hourly pay, including standard and overtime hours.
Regular pay: 40×$15.00=$600.0040 \times \$15.00 = \$600.00. Overtime pay: 8×($15.00×1.5)=8×$22.50=$180.008 \times (\$15.00 \times 1.5) = 8 \times \$22.50 = \$180.00. Total hourly pay = $780.00\$780.00.
You must isolate the hourly earnings from the total gross pay to determine how much money came from the piece-rate bonus.
2
Determine the total amount of the piece-rate bonus pool.
$1,060.00−$780.00=$280.00\$1,060.00 - \$780.00 = \$280.00
Subtracting the total hourly earnings from the total gross pay gives the exact amount earned purely from assembling extra units.
3
Determine the number of units eligible for the piece-rate bonus.
180−100=80180 - 100 = 80 units
The bonus is only paid for units produced that exceed the weekly quota of 100.
4
Calculate the bonus amount per excess unit.
$280.00÷80=$3.50\$280.00 \div 80 = \$3.50
Dividing the total bonus pool by the number of eligible units yields the individual piece-rate.

Key Concept

Calculating multi-component compensation by isolating variables (base pay, overtime, and piece-rate quotas).
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Topics

Wages, Salaries, and Commissions

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