SOLUTION: A bistro has decided to open an outdoor eating area along one wall of the building. The outdoor area will be rectangular. Assume the restaurant wants to maximize the outdoor area.

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Question 746303: A bistro has decided to open an outdoor eating area along one wall of the building. The outdoor area will be rectangular. Assume the restaurant wants to maximize the outdoor area.
A) Suppose there is 160 feet of fencing available for the three sides that require fencing. Write an equation to model this situation and explain your work
B) How long will the longest side of the fence be?
C) What is the maximum area?
Answer by Cromlix(4381) (Show Source):
You can put this solution on YOUR website!
using xm for the breadth of the bistro
and l for the length.
l = 160 - 2x for the perimeter.
The area = l x b
= l x b
= (160 - 2x)x
A(x) = 160x - 2x^2
A'(x) = 160 - 4x (Differentiated)
A'(x) = 0
160 - 4x = 0
- 4x = -160
x = 4
Using nature table:
- 4 +
160 -4x + 0 -
therefore x = 4 is a maximum.
Longest side will be 160 - 4x
160 - 16
= 144 feet
Maximum area = 160x - 2x^2
160(4) - 2(4)^2
640 - 32
608 ft^2