A homeowner has $360 to spend on building a fence around a rectangular garden. Three sides of the fence will be constructed with wire fencing at a cost of $2 per foot. The fourth side is to be constructed with wood fencing at a cost of $6 per foot. Find the dimensions of the rectangle that will maximize the area of the rectangle.

The width is 22.5 feet and the length 45 feet.

Step-by-step explanation:

Let l represent the length of the rectangle and  w represent the width of the rectangle. The cost of the fence (C) is:

C = 2l + 2w + 2l + 6w

C = 4l + 8w

360 = 4l + 8w

360 = 4(l + 2w)

90 = l + 2w

l = 90 - 2w

Area (A) of rectangle = length * width

A = l * w

Put l = 90 - 2w

A = (90 - 2w)w

A = 90w - 2w²

The maximum area is at A' = 0, hence:

Differentiating gives:

A' = 90 - 4w

Put A' = 0

0 = 90 - 4w

4w = 90

w = 22.5 feet

l = 90 - 2w = 90 - 2(22.5) = 45 feet

Hence the width is 22.5 feet and the length 45 feet.

10 - 75

step-by-step explanation:

there's nothing attached so it's most likely anything in that range.

below

step-by-step explanation:

1. 5/1

2. 10/16

3. 90/2

4. 1/20

5. 3/1

6. 14/24

7. 1/4

8. 18/10