A neighbor of mine has a lawn that isn’t looking too good. The picture below shows an image that’s similar to 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 estimate it at a quarter-acre lot.
• 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.