Quadratics

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• June 25th 2010, 06:45 AM
henry
Quadratics
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?

Thanks in advance
• June 25th 2010, 07:18 AM
skeeter
Quote:

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?

Thanks in advance

what do x and y represent?
• June 25th 2010, 07:25 AM
henry
i assume x and y represents the fences of the animal pens which is 2 pens high by 4 pens across
• June 25th 2010, 09:54 AM
earboth
Quote:

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?

Thanks in advance

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.