Question

A fence must be built to enclose a rectangular area of 20,000 ftsquared. fencing material costs $ 1 per foot for the two sides facing north and south and ​$2 per foot for the other two sides. find the cost of the least expensive fence.

Answer 1

The total cost of the least expensive fence would be $800.

To minimize perimeter and maximize area we take factors that are as close to equal as possible.  In this case, the closest whole number factors are 200 and 100.  Since the north and south faces cost less, we will make those 100 ft and make the more expensive east and west faces 200 ft.

100 ft × $2/ft = $200 per side × 2 sides = $400 for the north and south facing sides.

200 ft × $1/ft = $200 per side × 2 sides = $400 for the east and west facing sides

$400 + $400 = $800