Question

FAR = Floor Area Ratio

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.

a). What does your “optimal” density or FAR gradient look like?

Answer 1

Floor Area Ratio 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.

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

,

Where id distance in miles to the lift and is . The cost for construction is said to be 140 per square foot.

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

Mathemetially a square foot equals to , thus substituting the price and distance as,

.

We can re-write the equation as,

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