Posted by Willoby on .
A home gardener plans to enclose two rectangular gardens with fencing. The dimensions of the garden: x by 12x, y by 12xy
a. Find the values of x and y that maximize the total area enclosed.
b. What is the maximum total area enclosed?
c. How many meters of fencing are needed?

Math OPTIMIZATION 
Mgraph,
The total area A=A(x,y).
A=x(12x)+y(12xy)=12xx^2+12yxyy^2
Partial derivatives
A'x=122xy
A'y=12x2y
Solve the equations A'x=A'y=0 => a. x=y=4
b. Amax=32+16=48
c. 24+16=40 
Math OPTIMIZATION 
Willoby,
hey thanks! but where did you get 16 in b?

Math OPTIMIZATION 
Mgraph,
y(12xy)=4(1244)=16