Suppose a rectangular plot is to be fenced in, with the fencing on each of the four sides (labeled east, west, north, south) costing as follows: north: $4 per foot south: $5 per foot east: $3 per foot west: $5 per foot and the total cost of fencing is to be $700. What is the maximum area in ft2 of such a plot?

A = 1701,38 ft²

Dimensions:

x (north and south sides) = 38.89 ft

y (east and west sides) = 43,75 ft

Step-by-step explanation:

North and south (sides of same length) equal "y" cost (4 + 5) = 4,5 $/ft²

East and west (sides of same length) equal "x" cost (3 + 5) = 4 $ / ft²

Equation of cost is

C = Cost of (north + south) + Cost (east + west)

C = 2 * 4,5 * x + 4*2 * y

C = 9x + 8y

700 = 9x + 8y ⇒ y = (700 - 9x) / 8

A = x*y

A (x) = x * (700 - 9x) / 8

A (x) = (700 x - 9x²) / 8 A' (x) = (700 - 18 x) / 8 A' (x) = 0

(700 - 18 x) / 8 = 0 ⇒ 700 - 18 x = 0 ⇒ x = 700/18

x = 38.89 ft

y = (700 - 9x) / 8 ⇒ y = 349.99 / 8 ⇒ y = 43.75

And maximum ara is

A = x*y A = 38.89 * 43.75 = 1701,38 ft²