Question

There are economies of scale in ranching, especially with regard to fencing land. Suppose that barbed-wire fencing costs $21,000 per mile to set up.

Instructions: Enter your answers as whole numbers.

a. How much would it cost to fence a single property whose area is one square mile if that property also happens to be perfectly square, with sides that are each one mile long?

b. How much would it cost to fence exactly four such properties separately, which together would contain four square miles of area?

c. Now, consider how much it would cost to fence in four square miles of ranch land if, instead, it comes as a single large square that is two miles long on each side.

d. Which is more costly—fencing in the four, one-square-mile properties or the single four-square-mile property?

Answer 1

a) Cost of fencing one mile = $ 21,000

Cost of fencing the area of one square = Cost of fencing 4 mile as each side is one mile = 4 X $ 21,000 = $ 84,000

b) Cost of one square mile of area = $ 84,000

So, cost of four square miles of area = 4 X $ 84,000 = $ 336,000

c) Cost of fencing one side of large square with 2 miles long = 2 X $ 21,000 = $ 42,000

So, cost of fencing 4 sides of large square with 2 miles long = 4 X $ 42,000 = $ 168,000

d) Cost of fencing four is the costly.