A farmer is building a fence to enclose a rectangular area. The north side of the enclosed area

is against a building and requires no fencing. The west side of the enclosed area faces a highway and needs to

be reinforced with two layers of fencing. If the farmer wants to enclose $1200$ square feet, find the rectangular

dimensions that minimize the amount of fencing used and the minimum amount of fencing $($in feet$).$ Include

the feasible domain and verify the solution is a minimum