Friday

November 28, 2014

November 28, 2014

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

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 9:31amThe 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 7:31pmhey thanks! but where did you get 16 in b?

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

**Answer this Question**

**Related Questions**

Math - A gardenervhas 100 meters of fencing to enclose two adjacent rectangular ...

math - Vitaly and Jen have 24m of fencing to enclose a vegetable garden at the ...

Algebra - Algebra Word Problems: 1. The length of the floor of a one-storey ...

math - A gardener wants to use 62 feet of fencing to enclose a rectangular ...

Math - 1. A gardener has 140 feet of fencing to fence in a rectangular vegetable...

Math - A gardener has 120 ft of fencing to fence in a rectangular garden. one ...

math - a fencing company was asked to enclose three gardens with wire fences: a ...

algebra - A gardener has 120 ft of fencing to fence in a rectangular garden. one...

Math - The Kulas have decided to enclose their rectangular garden. The length of...

math - if a gardener fences in the total rectangular area shown in the ...