1. ## modeling with functions

I need help with this exercise. I don't know how to make the equation for the function ergo I don't know how the function

a rancher with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle

a) find a function that models the total area of the four pens
b) find the largest possible total area of the four pens

2. Originally Posted by cristinaivelisse
I need help with this exercise. I don't know how to make the equation for the function ergo I don't know how the function

a rancher with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle

a) find a function that models the total area of the four pens
b) find the largest possible total area of the four pens
1. Draw a sketch.

2. The complete area is calculated by: $A = l \cdot w$

3. The fencing consists of 2 lengthes and 5 width:

$2l+5w=750~\implies~w=150-\frac25 l$

4. Plug in this term into the equation of the area to get the equation of the function:

$A(l)=l\cdot \left(150-\frac25 l \right) = 150 l - \frac25 l^2$

5. The graph of the function is a parabola opening down with it's maximum value at it's vertex. Determine the coordinates of the vertex to get the value of l when the largest area occurs.
Spoiler:
I've got l = 187.5' and w = 75'