A metal box with a square base and vertical sides is to contain 1024 cm3 of water, the material for the top and bottom costs Rs 5 per cm2 and the material for the sides costs Rs 2.50 per cm2. Find the least cost of the box.

Explanation

`therefore` Volume of the box `V=bar{x}^{2} y=1024`



`Rightarrow quad y=frac{1024}{x^{2}}`



Let `C` denotes the cost of the box.



`therefore quad `


`C =2 x^{2} times 5+4 x y times 2.50`


...