dimension of garden with largest possible area?

Question

A rectangular garden next to a building is to be fenced on three sides. Fencing for the side parallel to the building costs $40 per foot, and material for the other two sides costs $40 per foot. If $2200 is to be spent on fencing, what are the dimensions of the garden with the largest possible area?

The parallel side =?
The other two sides =?

Answer 1

The question is confusing. Are you saying that the cost of material for all sides is $40 a foot?

In that case, the perimeter of the fence is 54 feet= 2O+P (O-length of cross sides,P-of the parallel side).
So we want to find the maximum area that meets this restriction. Area=O x P = O x (54-2O)=
54O-2O^2. dA/dO= 54-4O and the max is found for dA/dO=0. Then O=13.5 ft, and P=27 ft.

Answer 2

40L + 2*40W = 2200
L + 2W = 55
L = 55 - 2W
A = LW = 55W - 2W^2
For maximum area
W = 55/4 = 13.75 ft = 13 ft 9 in.
L = 55/2 = 27.5 ft = 27 ft 6 in.
A = 378.125 ft^2