A company is about to design a box to pack three circular objects. These objects have different radii; R1 = 6, R2 = 12, R3 = 16. The objective is to find the minimum dimensions for the box. In addition, the company does not like the objects to have overlap in the box. Formulate an optimization model to minimize the perimeter of the box.
Use Excel or AMPL (not the longhand format) to find the optimal solution.