Problem: Excavation, Backfill, and Cost Calculation for a Building Foundation

You are tasked with calculating the total costs associated with excavating a foundation for a building, the haul$-$off of excess soil, and the cost of the concrete to fill the foundation. You need to consider the following details:

Given Information:

Foundation Dimensions:

Length $=300$ feet

Width $=200$ feet

Depth $=4$ feet

Slope ratio for excavation sides $=1\mathrm{.}5$:$1($horizontal to vertical$)$

Material and Operation Costs:

Excavation cost: $5$ USD per cubic yard $($BCY$)$

Haul$-$off cost: $10$ USD per cubic yard $($LCY$)$

Concrete cost: $150$ USD per cubic yard $($BCY$)$

Load Factor $($LF$)=0\mathrm{.}70$: This accounts for the soil expanding when excavated.

Swell Factor $($SF$)=10\%$: This represents soil shrinkage when backfilled.

Tasks:

Calculate the total excavation volume $($including slopes$).$

Determine the backfill volume.

Calculate the haul$-$off volume.

Compute the total project costs for excavation, haul$-$off, and concrete.