Question

There are economies of scale in ranching, especially with regard to fencing land. Suppose that barbed-wire fencing costs $17,000 per kilometre to set up.

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

$ _______for the single one-square-kilometre property

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

$ _____ for four of the one-square-kilometre properties

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

$ _____ for the single four-square-kilometre property

d. Which is more costly—fencing in the four, one-square-kilometre properties or the single four-square-kilometre property?  (Click to select) : The single four-square-mile property , or Four one-square-mile properties

Answer 1

Barbed- wire fencing cost $17,000 per kilometre to set up.

a.

One kilometre One kilometre One kilometre One kilometre

Fencing cost per kilometre = $17,000

Single property – Perfect square – One kilometre long each side

4 sides each one kilometre long

Fencing cost = 4 * $17,000 = $68,000

Fencing cost = $68,000

b.

One-square-kilometre = $68,000

Each square is One-square-kilometre

4 squares are 4 square-kilometre

4 square-kilometre: Fencing cost = 4 * $68,000

Fencing cost = $272000

c.

Two kilometres Two kilometres Two kilometres Two kilometres

Single large square

One-kilometre fencing cost = $17,000

2-kilometre fencing cost = $17,000 * 2 = $34,000

Single large square – 2-kilometre-long each side

4 sides = $34,000 * 4 = $136000

Fencing cost = $136000

d.

Four - one square mile property is costly, because fencing cost is $272000 (which is high compred to the other two)