Question

A cuboidal shaped godown with square base is to be constructed. Three times as much cost per square meter is incurred for constructing the roof as compared to the walls. Find the dimensions of the go down if it is to enclose a given volume and minimize the cost of constructing the roof and the walls.

Answer 1

Let the length and breadth of the base = x.

Also let the height of the godown = y.

Let C be the cost of constructing the godown and V be the given volume.

Since cost is proportional to the area, therefore

C = k [3x² + 4xy], where k > 0 is constant of proportionality   …(1)

Substituting value of y from equation (3), in equation (1), we get

For maximum or minimum value of S

dC/dx = 0