In Singapore, commercial developments must comply with planning requirements that ensure adequate separation between buildings and roads while promoting a greener and more livable environment. These requirements include
common boundary setback to maintain appropriate building clearances from other developments and non-major roads, and peripheral planting verges (stretch of shrubs) to enhance landscaping,
green buffers (stretch of trees) and road buffers along major roads such as expressways, major or minor arterials.
The government also encourages tree planting at the rooftop of buildings to enhance environmental quality.
The dimensions of the requirements can be found in the tables below.
| Road Category | Major Road Buffer (inclusive of green buffer indicated in brackets) |
|---|
| Expressway | 15 m (3 m) |
| Major arterial | 7.5 m (3 m) |
| Minor arterial | 5 m (3 m) |
| Boundary | Minimum setback distance |
|---|
| Common boundary setback to maintain clearance from other commercial developments and non-major roads. | 3 m (including 2 m peripheral planting verge) |
Adrian bought a rectangular plot of land for commercial development as shown in the diagram (not drawn to scale). The land measures 118 m by 76 m, where the longer side faces the expressway. The other three sides are next to other commercial developments and non-major roads.
Show that the maximum floor area of a cuboid commercial building to be built on the rectangular plot of land, in compliance with Singapore’s planning requirements is \(6496\text{ m}^2\).[2]
The monthly maintenance cost (\(C\)) in dollars and the number of trees (\(x\)) are modelled by different functions for two companies.
Company A’s maintenance cost is represented as a linear function, shown on the graph below.
Company B’s maintenance cost and the number of trees are connected by the equation, \(C=0.005x^2-x+250\). Some corresponding values of \(x\) and \(C\) are given in the table below.
| \(x\) | \(0\) | \(100\) | \(200\) | \(300\) | \(400\) | \(500\) |
| \(C\) | \(250\) | \(200\) | \(p\) | \(400\) | \(650\) | \(1000\) |
Find the value of \(p\).[1]
Draw the graph of \(C\) against \(x\) for Company B for \(0\leq x\leq500\) on the grid below.[2]
Adrian researched on more information to help with his commercial development plan.
Formula to estimate the minimum number of trees and shrubs per dedicated area
\(\text{Minimum number of trees}=\dfrac{\text{Area of green buffer}+\text{Rooftop area for tree planting}}{20}\)
\(\text{Minimum number of shrubs}=\dfrac{\text{Area of peripheral planting verge}}{2}\)
All units for area are in square metre.
| Cost of installations for trees and shrubs |
|---|
| $180 per tree |
| $30 per shrub |
| Cost of monthly maintenance for trees and shrubs |
|---|
| For trees: refer to the graph above. |
| For shrubs: The cost of maintaining one tree is the cost of maintaining 5 shrubs. |
| No maintenance is required for all trees and shrubs during the first two months following installation. Maintenance shall begin from the third month after installation. |
Government sustainability grants
| Percentage, x, of rooftop area dedicated for tree planting | Grant awarded |
|---|
| \(x<40\%\) | $0 |
| \(40\%\leq x<60\%\) | $20 000 |
| \(60\%\leq x<80\%\) | $47 000 |
| \(x\geq80\%\) | $62 500 |
The building within the development shall be constructed based on the maximum floor area obtained in (a).
Adrian’s business partner says that if 60% of the rooftop area is dedicated for tree planting, the grant of $47 000 will be able to cover the trees and shrubs installation and maintenance costs within the first year of installation.
However, Adrian says that only by dedicating more area for rooftop tree planting, the higher grant of $62 500 will be able to cover the trees and shrubs installation and maintenance costs within the first year of installation.
Do you agree with Adrian or his business partner?
Justify the decision you made and show your calculations clearly.[5]