Answer to Question #99174 in Calculus for M

Question

MUST be answered in graphical format if possible!
Question:
A company is required to fence off the area around a robot arm to comply with health and safety law. They have 750m of fencing available...

The task is to find the maximum area they can fence off?

The answer also need to be presented in a graphical way if possible?

Answer 1

$Perimeter=2(x+y)=750$ m

$x+y=375$ m

$y=(375-x)$

$Area=xy$

$A=x(375-x)$

$A=375x-x^2$

For area to be maximum,

$dA/dx=375-2x=0$

$2x=375$

$x=375/2$ m

$A=375×375/4$

$A=35,156.25m^2$

In the graph,the intersection of graph xy=k and x+y=375

occurs at two points for different values of k.But when xy= k is tangent to the line,the value of k is maximum i.e. area of the fence is maximum.