Ushindi Ltd manufactures ornaments for export trade. Jobs are allocated to two operators, Mbotela and Juma, with bonus paid for hours saved. In the month of February 2009, Mbotela... Ushindi Ltd manufactures ornaments for export trade. Jobs are allocated to two operators, Mbotela and Juma, with bonus paid for hours saved. In the month of February 2009, Mbotela made 186 units and Juma made 210 units for which the time allowed of 30 standard minutes and 25 standard minutes per unit respectively was credited. The basic wage was ksh. 18 per hour for both employees. For every hour saved a bonus was paid at 20% of the basic wage rate. Hours worked in excess were paid at the basic wage rate plus two thirds. Mbotela completed his job in 44 hours and Juma completed his job in 39 hours. A basic working week has 40 hours. Required: For each operator, calculate: i. The amount of bonus payable. ii. The total gross wage payable. iii. The wages cost per unit. Read more

Steps to Solve

1. Mbotela Bonus Calculation

First, calculate the total standard time allowed for Mbotela's production: $ \text{Standard time allowed} = \text{Number of units} \times \text{Standard minutes per unit} $ $ \text{Standard time allowed} = 480 \text{ units} \times 15 \text{ minutes/unit} = 7200 \text{ minutes} $

Convert the actual time taken to minutes: $ \text{Actual time taken} = 9 \text{ hours} \times 60 \text{ minutes/hour} = 540 \text{ minutes} $ $ \text{Actual time for 5 days} = 540 \text{ minutes/day} \times 5 \text{ days} = 2700 \text{ minutes} $

Calculate the time saved: $ \text{Time saved} = \text{Standard time allowed} - \text{Actual time taken} $ $ \text{Time saved} = 7200 \text{ minutes} - 2700 \text{ minutes} = 4500 \text{ minutes} $

Calculate the bonus (30% of time saved multiplied by hourly rate): $ \text{Bonus} = 30% \times \text{Time saved} \times \text{Hourly rate in minutes} $ $ \text{Hourly rate in minutes} = \frac{\text{Hourly rate}}{60} = \frac{240}{60} = 4 $ $ \text{Bonus} = 0.30 \times 4500 \text{ minutes} \times 4 \text{ Ksh/minute} = 5400 \text{ Ksh} $

2. Mbotela Gross Wage Calculation

Calculate the basic wage: $ \text{Basic wage} = \text{Hours worked} \times \text{Hourly rate} $ $ \text{Hours worked} = 9 \text{ hours/day} \times 5 \text{ days} = 45 \text{ hours} $ $ \text{Basic wage} = 45 \text{ hours} \times 240 \text{ Ksh/hour} = 10800 \text{ Ksh} $

Calculate the total gross wage: $ \text{Gross wage} = \text{Basic wage} + \text{Bonus} $ $ \text{Gross wage} = 10800 \text{ Ksh} + 5400 \text{ Ksh} = 16200 \text{ Ksh} $

3. Mbotela Wage Cost per Unit

Calculate the wage cost per unit: $ \text{Wage cost per unit} = \frac{\text{Gross wage}}{\text{Number of units}} $ $ \text{Wage cost per unit} = \frac{16200 \text{ Ksh}}{480 \text{ units}} = 33.75 \text{ Ksh/unit} $

4. Juma Bonus Calculation

Calculate the total standard time allowed for Juma's production: $ \text{Standard time allowed} = \text{Number of units} \times \text{Standard minutes per unit} $ $ \text{Standard time allowed} = 560 \text{ units} \times 15 \text{ minutes/unit} = 8400 \text{ minutes} $

Convert the actual time taken to minutes: $ \text{Actual time taken} = 9 \text{ hours} \times 60 \text{ minutes/hour} = 540 \text{ minutes} $ $ \text{Actual time for 5 days} = (45 + 5) \text{ hours} \times 60 \text{ minutes/hour} = 50 \text{ hours} \times 60 \text{ minutes/hour} = 3000 \text{ minutes} $

Calculate the time saved: $ \text{Time saved} = \text{Standard time allowed} - \text{Actual time taken} $ $ \text{Time saved} = 8400 \text{ minutes} - 3000 \text{ minutes} = 5400 \text{ minutes} $

Calculate the bonus (30% of time saved multiplied by hourly rate): $ \text{Bonus} = 30% \times \text{Time saved} \times \text{Hourly rate in minutes} $ $ \text{Hourly rate in minutes} = \frac{\text{Hourly rate}}{60} = \frac{240}{60} = 4 $ $ \text{Bonus} = 0.30 \times 5400 \text{ minutes} \times 4 \text{ Ksh/minute} = 6480 \text{ Ksh} $

5. Juma Gross Wage Calculation

Calculate the basic wage for regular hours: $ \text{Regular hours} = 45 \text{ hours} $ $ \text{Basic wage} = \text{Regular hours} \times \text{Hourly rate} $ $ \text{Basic wage} = 45 \text{ hours} \times 240 \text{ Ksh/hour} = 10800 \text{ Ksh} $

Calculate overtime pay (time and a half): $ \text{Overtime hours} = 5 \text{ hours} $ $ \text{Overtime rate} = 1.5 \times \text{Hourly rate} = 1.5 \times 240 \text{ Ksh/hour} = 360 \text{ Ksh/hour} $ $ \text{Overtime pay} = \text{Overtime hours} \times \text{Overtime rate} $ $ \text{Overtime pay} = 5 \text{ hours} \times 360 \text{ Ksh/hour} = 1800 \text{ Ksh} $

Calculate the total gross wage: $ \text{Gross wage} = \text{Basic wage} + \text{Overtime pay} + \text{Bonus} $ $ \text{Gross wage} = 10800 \text{ Ksh} + 1800 \text{ Ksh} + 6480 \text{ Ksh} = 19080 \text{ Ksh} $

6. Juma Wage Cost per Unit

Calculate the wage cost per unit: $ \text{Wage cost per unit} = \frac{\text{Gross wage}}{\text{Number of units}} $ $ \text{Wage cost per unit} = \frac{19080 \text{ Ksh}}{560 \text{ units}} = 34.07 \text{ Ksh/unit} $