Question below:

Question

My friend has $312 to spend on a fence for her rectangular garden. She wants to use cedar fencing which costs $10/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?

area = _____ yard-squared

(step by step would be very helpful to understand)

Answer 1

312 = 10x + 3x + 3y + 3y

=13x +6y= 312

x = (312-6y)/13

A = xy = 312y/13 - 6y^2/13

A' = 312/13 - 12y/13 = 0

12y = 312

y = 312/12 = 52/2 = 26 yards for 2 sides costing $3 per yard

x = (312-6(26)/13 = (312-156)/13 = 56/13 = 4 4/13 yards on the 1 side costing $10 and on the same length side costing $3

A= 26(56)/13 = 112 square yards maximum