Answer:
- $1680 with no overtime
- $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.