Question

Optimization

Answer 1

Answer:

length = 100 m

width = 63.66 m

Step-by-step explanation:

Let's call

x: lenght of rectangle

y: width of rectangle, and also diameter of the semicircles

Perimeter: 2*x + π*y = 400

or:

x = 200 - π/2*y

Area of the rectangle = x*y

Replacing:

A = (200 - π/2*y)*y

A = 200*y - π/2*y²

At the maximum:

dA/dy = 200 - π*y = 0

y = 200/π

y = 63.66 m

and

x = 200 - π/2*63.66

x = 100 m