Question

Solve the problems below that pertain to optimal construction of an object. A warehouse is to be built in the shape of a rectangular solid with a square base. The cost of the roof per unit area is three times that of the walls, which we call W. Find the shape which will enclose the maximum volume for a given cost C??

Answer 1

2^a+1=3^2 hence 2^(a+1)/2=3
same 2^(b-1)/3=3 hence a+1/2=b-1/3

Answer 2

base =a height =h
let cost of wall per unit area=x
cost of roof per unit area =3x
a*a*3*x+4*b*a*x=c

max a*a*b
max a*a*(c-x*3a^2)/4x
Differentiating wrt a
a=sqrt(c/6x)
The b can be obtained by subtituting in earlier expression