Complimentary samples
Advertising is the very soul of trade, but it has costs!
Your advice is needed again to choose a nice (and cheap!) packaging for some complimentary boxes, containing a smaller version of the pasta that you have created.
Option no. 1 - Cylindrical boxes
These complimentary boxes will be shaped as small cylinders, having a volume of cm3.
The top and the bottom will be transparent, made with a plastic material that costs €2/m2, and the side is made with fine cardboard, that costs €10/m2.
Find the radius r of the base and the height h of the box that minimize its cost.
Option no. 2 - Rectangular parallelepiped
These classic complimentary boxes will be shaped as rectangular parallelepipeds, having the same volume of the cylindrical ones, and height 4 cm.
They will be built using the same materials for the top and the side as the cylindrical ones.
Find the length l and width w of the base of the box that minimize its cost. What do you observe?
Compare costs, and decide
How much does a cylindrical box cost? And the "classic" one? (Round costs to 2 decimal places) So the cheapest complimentary box is...