Optimiation Question?

Question

A farmer wants to build a rectangular fence. 3 sides will be made out of cement and cost $10/feet. 1 side will be made out of bricks and will cost $30/ feet. The area is to be 20 ft^2. Minimize the cost.

I meant 200 square feet.

Answer 1

let x = one side
y = perpendicular side
40x + 20y = C
xy = 20
y = 20/x
40x + 400/x = C
40x^2 - Cx + 400 = 0
dC/dx = 40 - 400/x^2
40x^2 = 400
x^2 = 10
x = √10 ≈ 3.162278 ft.
y = 2√10 ≈ 6.324555 ft.
C = 40√10 + 40√10 = 80√10 = $252.98(22)

40*3.17 + 400/3.17 = 252.9830
40*3.15 + 400/3.15 = 252.9841

Answer 2

C = 30 x + 10 [x + 2y] and xy = 20 yields a solution of x = 4 & y = 5

Answer 3

C=30x+10x(2y)
C=30x+20xy
A=xy
20=xy
y=20/x

C=30x+20xy
C=600/y+400
0=600/y+400
y=6/4

.....give up
0= -600y/y^2

2*
y=0