# DETERMINATION OF THE SHAPE OF THE CAN ECONOMICALLY USING THE CONCEPT OF MINIMUM SURFACE AREA

By: Al Azhary Masta,S.Si and Leli Nur Lathifah,S.Pd

Abstract

The economic principle states that production is done on the principle of using the smallest amount of capital to achieve the most profit. This principle is certainly used by goods production companies, one of which is cans.
Based on that principle, the company must make a business that can bring a big profit, one of which is by suppressing production costs. The cost of production of cans is assumed to be largely contributed by the cost of providing raw materials. Therefore, there is a calculation to find the necessary size of the can so that it requires minimum raw materials, this is the role of mathematics to solve the problem.
Looking at the reality in the field, there is a diversity of canned shapes, namely tube-shaped (circular plinths) and block shapes (rectangular plinths). By using the concept of derivatives are searched sizes that can minimize the necessary materials. For tube-shaped cans, the material used will be minimum if the height of the tube (h) is equal to the diameter (d). as for beam-shaped cans, the material used will be minimum if the length (p), width (l), and height (t) are the same. In other words, the beam must be cube-shaped. If a comparison is made between the tube and the cube, with the same volume the surface area of the tube is more minimum compared to the surface area of the cube.

Keywords : Shape, Minimum