Answer
$(a)$ $A=-\frac{5}{2}x^2+375x$
$(b)$ $A=14062.5ft^2$
Work Step by Step
Let the length of the rectangle be $x$ $ft$.
So, including all the parallel divisions and the $2$ side of the rectangle (which are $xft$), we have fencing of $5xft$
Width of the rectangle will be $\frac{750-5x}{2}ft$
Given the above information, we have the total area of rectangle :
$A=x\times \frac{750-5x}{2}=\frac{-5x^2+750x}{2}=-\frac{5}{2}x^2+375x$
$a=-2.5$
$b=375$
Since the value of $a$ is negative, we have maximum value of the function at $x=-\frac{b}{2a}$
$x=-\frac{375}{-2.5\times2}=\frac{375}{5}=75$
Length is $75ft$
Width is $\frac{750-5\times 75}{2}=187.5ft$
So, the largest possible total area of four pens will be :
$A=75\times 187.5=14062.5ft^2$
