Designing the Perfect Can 

Let us put it all together to understand how simple using optimization software really is. Having read the can design problem, you may have wondered how you are supposed to come up with an optimal design, especially since your marketing department has let you know that your can may only have a certain maximum diameter so that it fits neatly into your customers' hands, and a maximum height so the can will fit into the shelves.

Well, let us model this problem together. We are given: the volume V that must fit into the can, and the maximum diameter D and a maximum height H. A quick search on the web returns the formulae for the volume and surface of a cylinder: Volume = diameter^2 * height * PI / 4, Surface = diameter * PI * ( height + diameter/2):

Decision Variables

  1. (name: height, type: continuous, lower bound: 0, upper bound: H) 
  2. (name: diameter, type: continuous, lower bound: 0, upper bound: D)


V = diameter^2 * height * PI / 4  


Minimize  diameter * PI * ( height + diameter/2)


And that is all there is to it. What you see above is called a model and it specifies exactly the three types of information the machine needs to make a recommendation: What decisions do you need to make? What decisions are legal? What are you trying to optimize? Equipped with just this information, InsideOpt Seeker will prescribe the values for the diameter and the height of your can. 


Congratulations! You have just learnt one of the most powerful technology concepts in existence. Companies that use optimization technology -  like Microsoft, Shopify, FedEx, Air France, or the National Football League - are more efficient and always have an edge on their competition. 

Your next step is very simple: Contact one of our specialists at We provide a cutting edge optimization solver, and we are also available for consulting.