Perform calculations for project planning and cost analysis

2. Top One Cleaning Company is sub-contracted to remove debris of three construction sites.
The charges for each site include a standard charge (S) of $4,000 for removing debris, labour
costs (L) of $x per labour for debris removal and a hire cost for the number of bins (B) they
supply at $y per bin.

(a) Given that the total cost (T) include for all 3 sites is $108,800 when 10 labours
removed 120 bins of debris from the site and the cost (T) become $208,600 when 20 labours
removed 90 bins of debris from the sites, find x & y.

(b) If one of the sites removed 30 bins of debris, and the company expected to control the
cost in this site is less than $30,000, calculate the number of labours hire for debris removal.

3. To avoid nearby resident complain the noise made by the construction, the Construction
company need to measure the noise produced by the site at different places. The sound
intensity level ,3 (dB) of one of the company’s construction sites is a function of the sound
intensity I (Wm’2) of the site. The function is given by

10 1 I

EU) – » og 19.13

(a) What is the sound intensity level of the site if the sound intensity of the site is 300
Wm’2. Give your answer in form of a log 3 + b, where a and b are constants.

(b) In the evening, the sound intensity level is 50 dB, whereas the sound intensity level
during the day-time increases by 30 dB. How many times is the sound intensity of the
construction site during the day-time to that in the evening?

(c) Sketch the graph of ,B(I) against 1.

The sound intensity I also depends on how far away from the sound source. If the distance

of a building from the construction site is d (m), the sound intensity obtained in the building
in the evening can be given by a fimction of

ifé} = (4x1o3}e“3=”*5
(d) Calculate the distance between the building and the construction site.

(e) Sketch the graph of I(d) against



Solve surveying problems lP2.1]

4. In the figure, ABCD is an Art Museum. A vertical pole CD stands on the horizontal ground
ABC. The top of the pole D is due north of A and the angle of elevation of D from A is 45°.
The bearing and the angle of elevation of D from B are N60°E and 30° respectively. If AB
5om, and let CD = h, find

(a) AC and BC in terms of h

(b) ABCA

(c) CD 0

(d) the compass bearing and true bearing of A from B.

(e) total surface area of the Museum

(1) the volume of the Museum

(g) the polar co-ordinate of B if the co-ordinate of C is (0,0) N

(Give your answers correct to 2 significant figures.) I C
B _ _ _ _ _ _ _ I
50 m A
Perform calculations to support setting out procedures lP2.2l
6. To construct a straight
road between AB, soil I
is cut and the hole II is A I B
filled by the excavated
soil 1. The information is II
given as follow
Dimension : 8 m (wide) x 1600 m (long)
Cost of Cut : $ 350 / m3
Cost ofFil1 : $ 120 / m3
Cost of Impact soil : $ 100 / m3
Cost of Disposal : $ 150 / m3
(a) Complete the table above.
(b) Calculate the volume of earth to be cut and fill respectively.
(c) Calculate the volume of soil to be imported to the site or disposed from the site.
(d) Calculate the total cost of the earthwork.


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