Im having a bit of trouble with the following question, can anyone help?
800m of fencing are used to construct 8 rectangular animal pens.
a) show that y=800-12x
10
b) find the area A, of each pen, in terms of x.
c) find the dimensions of each pen when each is a maximum
d) what is the maximum are of each pen?

2. Originally Posted by henry
Im having a bit of trouble with the following question, can anyone help?
800m of fencing are used to construct 8 rectangular animal pens.
a) show that y=800-12x
10
b) find the area A, of each pen, in terms of x.
c) find the dimensions of each pen when each is a maximum
d) what is the maximum are of each pen?

what do x and y represent?

3. i assume x and y represents the fences of the animal pens which is 2 pens high by 4 pens across

4. Originally Posted by henry
Im having a bit of trouble with the following question, can anyone help?
800m of fencing are used to construct 8 rectangular animal pens.
a) show that y=800-12x
10
b) find the area A, of each pen, in terms of x.
c) find the dimensions of each pen when each is a maximum
d) what is the maximum are of each pen?

1. According to the given result the pens are arranged as shown in the sketch (see attachment).

2. You've got 3 rows of 4 xs each : 12x;
you've got 5 columns of 2 ys : 10y.

3. According to the text of the question you know:

$12x+10y=800~\implies~\boxed{y = \frac{800-12x}{10}}$

4. The area of one pen is calculated by: $A = x \cdot y$.

Plug in the term of y into this equation and you'll get a function in x:

$A(x)=x \cdot \frac{800-12x}{10}~\implies~A(x)=80x-\frac65 \cdot x^2$

5. This is the equation of a parabola opening down which has it's maximum at it's vertex. I don't know which method you want to use to determine the coordinates of the vertex (Completing the square, differentiation, ...)

6. The y-coordinate of the vertex gives the maximum area of one pen, the x-coordinate gives the length of the pen. Calculate the width by the given equation.