two adjacent rectangular garden is to be encolsed by a 400meters of fencing. find the dimensions of the garden to obtain a maximum area

Question

two adjacent rectangular garden is to be encolsed by a 400meters of fencing. find the dimensions of the garden to obtain a maximum area

Answer 1

x: total width of garden area (in m). y: total length of garden area (in m) (each rectangle will be x/2 by y m)

Constraint: 2x + 3y = 400 y = (400 - 2x)/3

Area = x · (400 - 2x)/3 = -2/3·x² + 400/3·x

The area function graphs as a concave down parabola, which will have its vertex (maximum) at x = - b/2a:

x_ideal = - (400/3) / (-4/3) = 100 y_ideal = 200/3