Question

In a site, 100m x 40m of earth is to be stripped to 0.5 m and to be moved 350m. The costs for some plants are given below:

Bulldozer: $y/m3 for first 100m then $2.1y/m3 for each extra 100m; Scraper: $1.5y/m3 per 100m; and Loader & Truck: $3.5y/m3 for first 100m then $0.5y/m3 per extra 100m.

Which method is the cheapest for moving the earth the 350m?

Question 10 options:

	A. Bulldozer
	B. Scraper
	C. Loader and Truck
	D. Either B or C

Answer 1

In the given situation total area of excavation is 100m*40m and delpth of excavation is 0.5 m.

thus, total volume of exacation of earth is 100*40*20= 2000m³

This 2000m³ of excavated earth need to move 350 m.

We have three option of Buldozer, Scrapper , Loader and truck.

Rate analysis of all this options are as follow:

(1) Bulldozer:

Given Rate:

For first 100 m .....$y/m³

For rest of length its rate is $2.1y/m³

here we consider length of 400 m because rate will calculated for 100m.

We need to transport earth 350 m but we need to pay for 400 m ( if this condition is not applied thus we can find out cheapest option by assuming rate for 400m)

Rate of Bulldozer = $(Y+2.1Y+2.1Y0+2.1Y)/m³.........(for first 100+rest of 300 m )

= 7.3 Y/m³ $

= 7.3Y*2000 = $ 14600 Y

(2) Rate for Scraper: = $1.5Y/m³

= (1.5 Y +1.5Y+1.5Y+1.5Y)/m³

= 6*2000 Y

= $12000Y

(3) Loader and Truck:

Rate for loader and Truck = (3.5Y+0.5Y+0.5Y+0.5Y)/m³

= 5Y*2000

=$10000 Y

from all these options Loader and truck is cheapest option.