Jim wants to build a rectangular parking lot along a busy street but only has 1400 feet of fencing available. If no fencing is required along the street, find the maximum area of the parking lot.
la console . it says your answer is wrong. maybe you forgot that their is no fencing along the street?
also it has to be a rectangle
w: width of the parking
ℓ: length of the parking
The perimeter of the parking is the length of the fence:
2.(ℓ + w) = 1400
ℓ + w = 700
w = 700 – ℓ
The area of the parking is:
a = w * ℓ → you know that: w = 700 – ℓ
a = (700 – ℓ).ℓ
a = 700ℓ – ℓ² ← this is a function of ℓ
You can get the maximum of a function when its derivative is null.
a’ = 700 – 2ℓ → then you solve the equation: a’ = 0
700 – 2ℓ = 0
2ℓ = 700
→ ℓ = 350
Recall: w = 700 – ℓ → w = 700 – 350 → w = 350
You can see that: ℓ = w = 350
So the maximum of the area of the parking is when the parking is a square.
The area is: 350 * 350 = 122 500 ft²
It might be possible for sure