Necessary Conditions: What Is the Point? The aim of this introduction to optimization is to give an informal first impression of necessary conditions, our main topic. Six reasons to optimize Exercises. Suppose you have just read for the first time about a new optimization method, say, the Lagrange multiplier method, or the method of putting the derivative equal to zero. At first sight, it might not make a great impression on you. So why not take an example: find positive numbers x and y with product 10 for which 3x + 4y is as small as possible. You try your luck with the multiplier rule, and after a minor struggle and maybe some unsuccessful attempts, you succeed in finding the solution. That is how the multiplier rule comes