A landscape designer has to design a rectangular pad of concrete at the centre of a rock garden. The lenght must be less than or equal to twice the width; the perimeter must be less than or equal to 40 m; and the area must be greater than or equal to 60 m².
1.)Write as system of inequalities to represent the constraints in this problem situation.
x=width y=length
y<=2x
2(x+y)<=40
xy>=60
The system of inequalities to represent the constraints in this problem situation is as follows:
y ≤ 2x (The length, y, must be less than or equal to twice the width, x.)
2(x + y) ≤ 40 (The perimeter, which is 2 times the sum of the width and length, must be less than or equal to 40 m.)
xy ≥ 60 (The area, which is the product of the width and length, must be greater than or equal to 60 m².)