A neighbor of mine has a lawn that isn\'t looking too good. The picture below sh
ID: 803864 • Letter: A
Question
A neighbor of mine has a lawn that isn't looking too good. The picture below shows an overhead image of his house and yard.
He has decided to remove all the old sod (grass), bring in a new 4 inch layer of topsoil, install new in-ground sprinklers, and reseed the lawn. He seems to think that he'll be able to save money by hauling loads of topsoil from the store himself in his pickup truck, rather than paying for delivery, but I don't think he's right. You're going to help us settle this.
Here is (most of) the information you asked for:
Is he redoing the whole yard or just the front?
He's redoing the whole yard
How much topsoil does he need?
I'm not sure, you'll have to figure that out. Remember he's putting a new 4 inch layer down over all the area currently covered by grass in the overhead picture above.
How big is the yard?
I'm not sure, but you can probably estimate it using the overhead picture.
What kind of pickup truck does he drive?
A 2003 Ford F-150 XL.
How much can the pickup carry?
The truck bed is 80 inches long, 69 inches wide, and 20 inches tall.
How much is the delivery charge?
$30 per truckload on top of the soil cost. Each truckload can deliver up to 18 cubic yards.
How much does the topsoil cost?
$18 per cubic yard (sold in 1/4 yard increments).
How far is the soil store?
It is 9 miles away. It takes about 20 minutes to drive there.
What gas mileage does the pickup truck get?
It averages 17 miles to the gallon.
What is the current gas cost?
Assume it's $3.79/gallon.
Using this information, figure out whether my neighbor will save money by picking up the soil himself. Use the results of your calculations to guide your decision: would you recommend that my neighbor pick up the soil himself, or pay for delivery?
Detail all your assumptions and calculations, and clearly write out your final conclusions.
Explanation / Answer
How much topsoil does he need?
The topsoil requirement:
Lawn Area: = Backyard Area + Front yard Area + Side Yard Area
Backyard Area: =75*25 feet
= 1875 Feet
Front yard Area = (45*25) + (5*10)
= 1175 Feet 3
Side Yard Area = 25*20
= 500
Lawn Area: = 1875 + 1175 +500
= 3550 feet3
Topsoil Volume: = Lawn area * topsoil height* Topsoil density
= 3550 * .33* 2.4 (2.4 topsoil density) feet3
= 2811.6 feet3
= 234.3 Yard3
Topsoil volume required in yard = 234.3 Yard3
Pickup Volume capacity- =6.66*5.75*1.66 feet3 (convert the truct dimension into feet from inches)
=63.569
Pickup carrying capacity = Volume capacity* density
= 63.569* 2.4
= 152.5673 feet3
Pickup Actual capacity = Carrying Capacity* fill factor
= 152.5673*.8 (fill factor 80%)
= 122.0538 feet3
= 4.52 Yard3
Delivery Charge = No of truckloads* delivery charge per truckload
No of Truckloads = (234.3/18)
= 13.01
= 14
Delivery Charges = 420 $
Topsoil Cost
= Topsoil Volume * Charges per cubic yard (in ¼ yard increments)
=(234*18)+4.5 $ (4.5 is the charge of .3 yard)
= 4216.5 $
Cost incurred on transporting tops soil using pickup
Store distance - 9 miles
Total topsoil volume- 234.3 yard3
Pickup capacity- 4.52 Yard 3
Total Distance - = (Total topsoil volume/pickup capacity)* (To & Fro store distance)
= (234.3/4.52)*(18) miles
= 933.05 miles
Fuel Requirement = Total Mileage / (Average Mileage per gallon) gallons
= 933.05/ 17 gallons
= 54.88 gallons
Fuel Cost = (Fuel Requirement * Cost per gallon) $
= 54.88*3.79 $
= 208.016 $
Actual Saving/Loss- = Delivery charges using truck - Fuel cost of Pickup
= 420 - 208.016
= 211.984 $
Conclusion: He can save 211.984 $ by using his pickup truck for topsoil transportation. So he should use his pickup for transporting the topsoil.
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