Question

the material for the bottom of a rectangular box costs 3 times as much per square foot as the material for the side and top. find the greatest capacity such a box can have if the total money available for material is $12 and the material for the bottom costs $0.60 per square foot.

Answer 1

if we assume x=width, y=length, z=height;is it correct to form the constraint as \[g(x,y,z)=(2xz+2yz+xy)0.2 + xy(0.6)-12?\]

Answer 2

that looks good to me, but how do you maximize xyz?

Answer 3

owh k. just wanted to check on the constraint before proceeding. i'll let \[f(x,y,z)=xyz\]then \[\nabla f=\lambda \nabla g\]