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224 hours are required to complete a project.4 men are employed for this project.

1: the hourly rate of each man is 750$. if the 4 men do not work overtime, find the total amount paid to the men.
2: their normal working hours are from 9 am to 6 pm with a hour long lunch break. given that their overtime rate is 1.5 times their hourly rate, find the total amount to be paid to the 4 men if the project is completed in 4 days. (please show working)

User Stevevls
by
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1 Answer

4 votes

Answer:

  1. $1680 with no overtime
  2. $2040 for completion in 4 days

Explanation:

You want the payroll costs for a 224-hour project completed by 4 men, both without and with overtime pay.

1. Straight time

The payroll cost for a 224-hour project with workers paid $7.50 per hour will be ...

($7.50/h) × (224 h) = $1680

The total amount paid to the men will be $1680.

2. Overtime

From 9 am to 6 pm is 9 hours. Deducting an hour for lunch leaves 8 straight-time hours per day. 4 men working 4 days will put in ...

(4 men) × (8 h/day/man) × (4 days) = 128 hours . . . . straight time

Completion of the 224-hour project in that time will require ...

224 -128 = 96 . . . . . hours of overtime

The overtime hours get paid at a 50% premium, so effectively require pay for additional hours of ...

(96 h) × 50% = 48 h . . . . . added payroll cost

The payroll for 4 men for working 224 hours in 4 days will be ...

(224 h +48 h) × $7.50 = $2040

The total paid to the men for completion in 4 days will be $2040.

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Additional comment

The expression for the pay with overtime could be written ...

men × days × pay per man-day

4 × 4 × (8 × $7.50 + (224/16 -8) × 1.5 × $7.50)

Using the commutative and associative and distributive properties of arithmetic, this can be evaluated many different ways.

We have rearranged it to ...

$7.50 × (16×8 + 224 -16×8 + 0.5(224 -16×8)) = $7.50(224 +0.5(96))

We have interpreted "750$" to mean $7.50. If each man actually gets paid a rate of $750 per hour, then the totals get multiplied by 100:

$168,000 for no overtime

$204,000 for overtime

This may be the case after a few years' inflation. We know some professionals get paid perhaps $400 per hour, so it is not too much of a stretch to imagine $750 per hour for some highly specialized tasks.

User Sharathi RB
by
7.3k points
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