Posted by **Willoby** on Saturday, September 3, 2011 at 1:47am.

A home gardener plans to enclose two rectangular gardens with fencing. The dimensions of the garden: x by 12-x, y by 12-x-y

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**, Saturday, September 3, 2011 at 9:31am
The total area A=A(x,y).

A=x(12-x)+y(12-x-y)=12x-x^2+12y-xy-y^2

Partial derivatives

A'x=12-2x-y

A'y=12-x-2y

Solve the equations A'x=A'y=0 => a. x=y=4

b. Amax=32+16=48

c. 24+16=40

- Math OPTIMIZATION -
**Willoby**, Saturday, September 3, 2011 at 7:31pm
hey thanks! but where did you get 16 in b?

- Math OPTIMIZATION -
**Mgraph**, Sunday, September 4, 2011 at 6:24am
y(12-x-y)=4(12-4-4)=16

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