SOLUTION: My friend has $270 to spend on a fence for her rectangular garden. She wants to use cedar fencing which costs $15/yard on one side, and cheaper metal fencing which costs $3/yard fo
Question 1100148: My friend has $270 to spend on a fence for her rectangular garden. She wants to use cedar fencing which costs $15/yard on one side, and cheaper metal fencing which costs $3/yard for the other three sides. What are the dimensions of the garden with the largest area she can enclose?
length for cedar side = _____yard
width for other side = ______yard
What is the largest area that can be enclosed?
I NEED ASAP PLEASE Answer by ikleyn(52777) (Show Source):
Let x be the length in yards of the front fence (at 15 dollars per yard).
Then the other dimension will be yards, or yards = (45 - 3x) yards.
The area is the product of these dimensions
Area A = square yards.
And the problem asks to find the maximal area as the maximum of this quadratic form.
This quadratic form has the zeroes 0 and = 15, so its maximum is achieved exactly at the midpoint between the zeroes, i.e at x= 7.5.
Answer. Under the given condition, the maximum area is the rectangle with one dimension 7.5 yards (front yard at $15/yard)
and other dimension 45-3*7.5 = 22.5 yards.
