Calculus question please show all the work.

Question

you want to design a pen to hold your precocious goats. the pen is to be split into 4 areas of equal size, with the separation fences all running parallel. if you have 120 meters of fencing. write the equation you need to use to maximize the area.

write the equation you need to use to maximize the area.

b.) write out the constraints for the problem.

c.) what are the outside dimensions of the pen?

Answer 1

2L + 4w = 120

L + 2w = 60

L = 60-2w

Area = w * L = w * (60-2w) = 60w - 2w^2 = A(w)

0 = dD/dw = 60 - 4w

4w = 60

w=15

4(15) + 2L = 120

60 + 2L = 120

2L = 60

L = 30

Max area is 450