please answer all parts as fast as possible 7.A rancher want to enclose three rectangular areas in a field, one for sheep, one for cattle, and one forpigs. There are 240 meters of fencing available.(a) Let x and y be the dimension of each rectangular plot (see picture below). Find a formula for A(x), thetotal area of the three plots as a function of x.XyyyyXA(x) =(b) Compute A0 (x).A'(x) =(c) Find the critical point(s)critical point(s):(d) What dimensions yield the maximum area? What is this maximum surfacearea (of the 3 plots)? Do not forget the units!x =andy =andA =

Hi, thank you for the question. Since you have posted a question with multiple subparts, as per our policy we will answer only the first three parts. Kindly upload the question again specifying the part to be solved. From the figure note that, the field is in shape of a rectangle of width y and length 3x. It is given that 240 m of fencing is available. That is, P=240. (a) Recall the fact that the area of the rectangle of length l and width w is A=lw and perimeter is 2(l+w). Substitute P=240, l=3x,w=y in 2(l+w): 2(y+3x)=240y+3x=120y=120-3x Substitute l=3x,w=y and y=120-3x in A=lw: A=3x120-3x=360x-9x2 Therefore, Ax=360x-9x2. (b) Obtain the derivative of Ax=360x-9x2 as follows: A'x=3601-92xA'x=360-18x Therefore, A'x=360-18x. (C) Equate the first derivative to 0 to obtain the critical points as follows: A'x=0 360-18x=0 18x=360 x=20 The critical point is x=20.