Question

Floor Area Ratio (FAR)

You have purchased the land and lifts of an older ski resort. You are upgrading the lifts and are master planning the real estate development of the ski resort. After studying other resorts you come up with the following (back of the envelope) regression for the sales price per square foot of residential real estate in similar resorts:

P = 300 – 100d – 20F

Where d is distance in miles to the lifts and F is FAR. You ascertain that construction costs will be 140 per square foot regardless of FAR.

Given:

FAR Optimal Density Equation –

F = 160-100(3.587 ^e-8) / 20

Question:

With the Given Information and the Optimal Density Equation, what is the Optimal Point to extend development of the Ski Resort?

Answer 1

Given data:

Ø Floor Area Ratio (FAR) is observed as an inducement to vertical growth as compared to horizontal growth. According to the theory, Higher FAR has its own advantages and disadvantages.

Ø The Floor Area Ratio (FAR) of a project is an important indicator of the density of the project and how much a home there would cost. We explain what exactly the FAR is and its importance for home buyers

According to the question, the equation is given to be as,

P=300-100d-20F,

Where

d = distance in miles to the lift and

F = FAR.

The cost for construction = 140 per square foot.

Thus, an optimal FAR gradient would have an equation with minimum cost and distance irresecpetive of the function F.

The FAR of a project is the total floor area of the building (including the space covered by all the floors in the building) divided by the area of land on which the project is being constructed.

The FAR is decided by municipal corporations or the development authority, according to the Development Control Regulations (DCR) and varies from one city or even locality, to another

Mathematically a square foot equals to 3.587^ {e-8}, thus substituting the price and distance as,

140=300-100(3.587^ {e-8})-20F.

We can re-write the equation as,

F=\frac {160-100(3.587^ {e-8})}{20}

Hence the FAR will have an optimal density equation as shown above.