Split the problem into parts:

- what is the area of an equilateral triangle with side

?

- what is the volume of the prism you need, with height

and side

?

- what is the lateral area of this prism?

- express the price

in terms of

and

.

- given the volume

of the prism, express

in terms of

(and

, fixed). Use this to express the price in terms of

(and of

, which is fixed).

- study the price function you have obtained (depending on

): for which

is it minimum?, what is this minimum value? What is the value of

corresponding to that

?