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.(let w be the width of the rectangular area and A(w) be the area.)
b) find the largest possible total area of the four pens. (round your answer to one decimal place.)

Question

turingtest · Answer

is w the width of one side of the pen or rectangle?

anonymous · Answer

rectangle

turingtest · Answer

2(L+w)=750 represents how much fence he has
2L=750-2w ---> L=375-w
(L)(w)=area=375w-w^2=A(w) so there's your answer for (a)
to maximize a function, take its derivative and set it to zero:
A'(w)=375-2w=0
w=187.5
L=375-w=187.5=w, so it's a square
the maximum total area is L^2=w^2=187.5^2=35156.25 sqft
dividing this into equal quarters yeilds
35156.25/4=8789.0625 sqft for each pen

anonymous · Answer

thank you

anonymous · Answer

pretty sure this is wrong, i got the correct answer for (a) which isnt the one listed here and  i tryed inputting the answer you recieved for (b) and it was incorrect