A = x y
cost = 75 x + 60 y = 1750
60 A = x (1750 - 75 x)
maximize 60 A = z
z = 1750 x -75 x^2
75 x^2 -1750 x = -z
complete square to find vertex o parabola
x^2 - 23.3 x = -z/75
x^2 - 23.3 x + 11.7^2 = - z/75 + 136
(x -11.7)^2 = -(1/75)(z-10,200)
x = length = 11.7
A = z/60 = 170
so x y = 11.7 y = 170
y = width = 14.5
A farmer wants to fence a small rectangular yard next to a barn. Fence for side parallel to the barn will cost 75 per foot and the fence for the other two sides will cost 30 per foot. The farmer has a total of 1750 dollars to spend on the project. Find the dimensions for the yard that will have the largest possible area.
The side parallel to the barn should be feet long and the other two sides should be feet long each.
1 answer
3 answers