Question

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.

1] 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.)

2]Find the largest possible total area of the four pens. (Round your answer to one decimal place.)

Answer 1

divide the rectangle into four and label longest side as l and shortest side w then perimeter equal to the following:
3l+3w=750
we also know that the area is A=lw
to get area in terms of w solve for l in the perimeter equation and plug it in the area equation like the following:
l=(750-3w)/3=250-w
*A(w)=lw=(250-w)(w)=250w-(w^2)
for maximum area take derivative of A(w) and set it equal to zero like the following:
A'(w)=250-2w=0 now solve for maximum width
w=250/2=125 ft, and solve for l=250-w=250-125=125ft
so to get maximum area the width and length have to equal 125ft
and maximum area will be *A=lw=(125(125)=15625 ft^2

Answer 2

I dont think it is 3L+3W=750 it's going (2w+2L which is the perimeter + 3W(the fences that are parallel to the Length of the rectangle that split it into 4 pens)

Answer 3

so it should be 5w+2L=750 ?

Answer 4

other than that it would be correct