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Answer :
a)Total material to be excavated: 1,613 cubic yards
b) Number of days to complete the work: 11 days
c) Number of weeks to complete the work: 2 weeks
d) Labor and material cost: $17,600
e) Rate per cubic yard of material removed: $260
a) The volume of the lake:
Area of the lake = 1 acre
Average depth of the lake = 5 feet
Convert the area to square feet: 1 acre = 43,560 square feet
Volume of the lake = Area × Depth = 43,560 cubic feet
Convert the volume to cubic yards: 43,560 / 27 = 1,613 cubic yards
b) The number of days to complete the work:
The contractor can remove 150 cubic yards of material in 1 shift.
Divide the total volume of the lake by the amount removed in a shift: 1,613 / 150 = 10.75 ≈ 11 days
c) The number of weeks to complete the work:
The contractor removes 100 cubic yards of material per day for 2 days of the week.
The contractor removes 150 cubic yards of material per day for the remaining 5 days of the week.
Calculate the total amount of material removed in a week:
(100 × 2) + (150 × 5) = 950 cubic yards
Divide the total volume of the lake by the amount removed in a week:
1,613 / 950 = 1.7 ≈ 2 weeks (rounded to whole number)
d) The labor and material cost:
The cost of the operator and helper per hour is $200.
Calculate the total production:
Amount produced on Mondays and Fridays
=100 cubic yards per day × 2 days = 200 cubic yards
Amount produced on the remaining 5 days
= 150 cubic yards per day × 5 days = 750 cubic yards
Total production in the first week
= 200 + 750 = 950 cubic yards
The total hours worked in the first week:
Hours worked on Mondays and Fridays
= 2 days × 8 hours/day = 16 hours
Hours worked on the remaining 5 days
= 5 days × 8 hours/day = 40 hours
Total hours worked in the first week
= 16 + 40 = 56 hours
The labor and material cost in the first week:
Labor and material cost per hour = $200
Total labor and material cost in the first week
= 56 hours × $200/hour = $11,200
The amount produced in the second week and total hours worked:
Amount produced in the second week = Total volume - Amount produced in the first week
= 1,613 - 950 = 663 cubic yards
Total hours worked in the second week
= 3 days × 8 hours/day + 2 days × 8 hours/day = 32 hours
The labor and material cost in the second week:
Labor and material cost in the second week = Total hours worked in the second week × $200/hour
= 32 hours × $200/hour = $6,400
Total labor and material cost = Labor and material cost in the first week + Labor and material cost in the second week = $11,200 + $6,400 = $17,600
e) The rate per cubic yard of material removed:
A 30% markup is required.
Calculate the markup amount: 30% × $200 = $60
Calculate the rate per cubic yard: $200 + $60 = $260 per cubic yard
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