The fencing of the left border costs $4 per foot, while the fencing of the lower border costs $1 per foot. (no fencing is required along the river.) you want to spend $64 and enclose as much area as possible. what are the dimensions of your garden, and what area does it enclose? hint [the area of a right-triangle is given by

Answer

Left border = 8 feet

Lower border = 32 feet

Area=128 〖ft〗^2

Explanation

The area is a right triangle.

Let us take the left border to be y feet and the lower border to be x feet

Area=1/2 yx

The cost of fencing would be 4y+x=64.

From this expression x=64-4y

Substituting this value of x in the area we have;

Area=1/2 y (64-4y)

A=32y-2y^2

To get the maximum area of the triangle the first derivative of the area would te equal to zero.

A=32y-2y^2

dA/dy=32-4y=0

4y=32

y=8

Since x=64-4y

x=64 - (4*8) = 32

The dimensions of the garden are 8 feet by 32 feet.

Since the garden is a right triangle,

Area=1/2*8*32

Area=128 〖ft〗^2