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
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
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:
4. The area of one pen is calculated by: .
Plug in the term of y into this equation and you'll get a function in x:
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.