Question

A large rectangular area is to be fenced off ( a large rectangle divided into 2 smaller rectangles). The fence used to divide the space cost $10 per foot and the fence used for the perimeter costs$15 per foot. If the total budget for the project is $60000 what are the dimensions that yield the largest area

Answer 1

Length of area is 857.14 ft

Width of area is 857.14 ft

Length of dividing fence is 857.14 ft

Explanation:

Here we have

Area of rectangle = Length × Width

The dimension, of the rectangle with the largest area is the dimension of a square, hence we have;

Length of rectangle = Width of rectangle = x

Hence, the perimeter of the area = 4·x, while the width of the dividing fence = x

Therefore, since the we have;

Cost of the perimeter fence = $15/foot

Cost of the dividing fence = $10/foot

Then;

4·x × 15 + x × 10 = 60000

60·x + 10·x = 60000

x = 60000/70 = 857.14 ft

Which gives the following dimensions;

Length of area = 857.14 ft

Width of area = 857.14 ft

Length of dividing fence = 857.14 ft.