Find the optimum design of the beer can problem in example 10.7 using a graphical method.

Data From Example 10.7:

Formulate a standard optimization problem for a beer can design problem. We want to design the beer can that can hold at least specific amount of beer and meet other design requirements. The goal is to minimize the manufacturing cost as they are produced in billions. Since the cost can be related directly to the surface area of the sheet metal used, it is reasonable to minimize the sheet metal required to fabricate the can. Fabrication, handling, aesthetic, and shipping considerations impose the following restrictions on the size of the can:
1. The can is required to hold at least \(400 \mathrm{ml}\) of fluid.
2. The diameter of the can should be no more than \(8 \mathrm{~cm}\). In addition, it should not be less than \(3.5 \mathrm{~cm}\).
3. The height of the can should be no more than \(18 \mathrm{~cm}\) and no less than \(8 \mathrm{~cm}\).
Following the three-step procedure, write a standard form of the optimization problem.