Step 1 :Given the total volume of earth to be moved is \(29,630 BCY\), the swell factor is \(25\%\), the project length is \(700 feet\), the project width is \(200 feet\), the cut is \(20 feet\) deep, the cut and fill area are both \(150 feet\) long, the material has an average weight of \(2,700 lb/cy\), the route between the cut and fill has an average slope of \(5\%\), and travel is uphill when loaded.
Step 2 :The cost per hour for the scraper is \$160.93 and the transport cost is \$7,500. The cost per hour for the dozer is \$210.85 and the transport cost is \$8,250.
Step 3 :Assuming the scraper speed is \(10 mph\), the scraper load capacity is \(20 cy\), the dozer speed is \(5 mph\), and the dozer load capacity is \(10 cy\).
Step 4 :Calculate the total time required for the scraper to move the earth by dividing the total volume of the earth to be moved by the capacity of the scraper per hour. The total time for the scraper is \(148.15 hours\).
Step 5 :Calculate the total time required for the dozer to move the earth by dividing the total volume of the earth to be moved by the capacity of the dozer per hour. The total time for the dozer is \(592.6 hours\).
Step 6 :Calculate the total cost for the scraper by multiplying the cost per hour by the total time and adding the transport cost. The total cost for the scraper is \$31,341.78.
Step 7 :Calculate the total cost for the dozer by multiplying the cost per hour by the total time and adding the transport cost. The total cost for the dozer is \$133,199.71.
Step 8 :Compare the total cost for the scraper and the dozer. The scraper is more cost-effective because its total cost is less than the total cost for the dozer.
Step 9 :\(\boxed{\text{Therefore, the CAT 623K elevating scraper is the best choice for the project.}}\)