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Answer:
The dimensions of the garden that minimize the cost is 9.018 feet(length) and 13.528 feet(width)
Step-by-step explanation:
Let the length of garden be x
Let the breadth of garden be y
Area of Rectangular garden =
We are given that the area of the garden is 122 square feet
So, ---A
A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft
So, cost of brick along length x = 20 x
On the other three sides by a metal fence costing $10/ft.
So, Other three side s = x+2y
So, cost of brick along the other three sides= 10(x+2y)
So, Total cost = 20x+10(x+2y)=20x+10x+20y=30x+20y
Total cost = 30x+20y
Substitute the value of y from A
Total cost =
Total cost =
Now take the derivative to minimize the cost
Equate it equal to 0
Now check whether it is minimum or not
take second derivative
Substitute the value of x
Since it is positive ,So the x is minimum
Now find y
Substitute the value of x in A
Hence the dimensions of the garden that minimize the cost is 9.018 feet(length) and 13.528 feet(width)