SOLUTION: A family wants to build a fence around a rectangular area of their backyard using their house as one side of the rectangle. The family has $2400 to spend on the fence and is consid

Algebra ->  Functions -> SOLUTION: A family wants to build a fence around a rectangular area of their backyard using their house as one side of the rectangle. The family has $2400 to spend on the fence and is consid      Log On


   

Question 1092840: A family wants to build a fence around a rectangular area of their backyard using their house as one side of the rectangle. The family has $2400 to spend on the fence and is considering using either a fence that costs $50 a yard or a fence that cost $60 a yard.
Suppose the family builds the fence using the $60 yard fence. Let x be the width of the enclosed rectangle. Using a function for the area of the enclosed rectangle, find the maximum area.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+2400%2F60+=+40+ yd of fence
+x+ = width
+40+-+2x+ = length
Let +A+ = area
+A+=+x%2A%28+40+-+2x+%29+
+A+=+-2x%5E2+%2B+40x+
The x-value for the maximum area is
given by the formula:
+x%5Bmax%5D+=+-b%2F%282a%29+
+a+=+-2+
+b+=+40+
+x%5Bmax%5D+=+-40%2F%282%2A%28-2%29%29+
+x%5Bmax%5D+=+10+ yds
----------------------------
Plug this result back into equation to get +A%5Bmax%5D+
+A%5Bmax%5D+=+-2%2A10%5E2+%2B+40%2A10+
+A%5Bmax%5D+=+-200+%2B+400+
+A%5Bmax%5D+=+200+ yd2
--------------------------
Here's the plot of the Area function:
+graph%28+400%2C+400%2C+-2%2C+25%2C+-20%2C+250%2C+-2x%5E2+%2B+40x+%29+