PLZ any one help dis question...?

Hi,

Let's use the Lagrange technique: Define "x"=width=length "y"=height. Thus (x^2)y=8 -> (x^2)y-8=0. This is the constrainment. The expression we need to minimize is ("z"=surface area) z=(x^2)+4xy. According to the technique we should now build the equation (x^2)+4xy-L[(x^2)y-8]=0 ["L"=Lagrange Variable].  The next step is to use a gradient on the latter equation and to look for critical points on equation with 0. So together with the constrainment we'll have 3 expressions:

(x^2)y=8

2x+4y-2xyL=0 

4y-Lx^2=0 

You should now solve these equations and substitute the numbers to the "z" equation. The last step is to choose the minimal result.

I'm sorry I couldn't bother to solve the equations.

i) 2 ii) 2 iii) 20 (Bottom (4) + 4 sides (each 4))