My favorite books in college were the linear algebra texts by Gilbert Strang. I found it more intuitive and relevant than other texts, and still enjoy thumbing through it when I'm pining for those halcyon days.

The thing I liked most about these books is that (especially at the time), they seemed like bread and butter mathematics. I imagined that someday in my career I would actually need to solve some optimization problem or at least a system of linear equations. Alas, I haven't ever had that joy, but maybe that's because I haven't looked for math problems to solve.

In the real world people don't bother solving their math problems - they just guess. I suspect that a part of that is that they don't really have any mathematical training and the other part is that their problems are just too hard. I also suspect that their guesses are generally pretty off the mark.

People guess solutions of complicated problems all the time and generally do a bad job of it. Once we get beyond the math of sums and averages our general perception of the world breaks down. Take the classic case of trying to guess the odds of two people in a cocktail party sharing the same birthday. It ends up being a %50 chance if there are 23 people in the same room.

Optimization can just as tricky - sometimes even trickier than probability, because there are often multiple solutions to a problem and many different factors that must be figured in. One of my New Years resolutions is quit guessing on problems that I come across and begin solving simplified versions with methods from the Strang books.

So in my initial feeble effort I solve a simplified problem of stocking shelf space in a grocery store. Grocers have fairly small percentage profit margins and so a small boost in real profit can add a lot to that percentage. I have a case where a grocer must decide on how much of two shampoo products they should display. The grocer wants to stack the shelf with a number of products that will maximize the profit within the constraints of demand, shelf space, and distribution. One product us a is a combination shampoo and conditioner in a small bottle. The other contains two separate bottles of shampoo and conditioner that are shrink wrapped together and thus take up more space on the shelf. The second is more profitable, because it costs more. The grocer must figure out how much to order on a weekly basis from the distribution center in order to maximize their profit. I solve the problem in Excel using methods from Strang's book. Here is the solution.