2 At a distance of x feet from the beach the price in dollar

2. At a distance of x feet from the beach, the price in dollars of a plot of land of area a square feet is f (a;x).

a) What are the units of fa( a;x)? What does fa(1000;300) = 3 mean in practical terms?

b) What are the units of fx(a;x)? What does fx(1000;300) =2 mean in practical terms?

c) Which is cheaper: 10005 square feet that are 305 feet from the beach, or 998 square feet that are 295 feet from the beach? Justify your answer using local linearization

Solution

Price (f) is a function of 2 variables that is area \'a\' (sq fts) and distance \'x\' feet from the beach.

a) Units of fa(a,x) will be dollars/foot

so fa(1000;300) = 3 means that the price of land in dollars which is of 1000 square feets and is at 300 feets distance from the beach will be 3 dollars/foot.

b) Units of fx(a,x) will be dollars/square foot

so fa(1000;300) = 3 means that the price of land in dollars which is of 1000 square feets and is at 300 feets distance from the beach will be 2 dollars/sqaure foot.