Let's say you own a company that makes bolts that are used on the International Space Station! These bolts have very specific requirements but two of the most important requirements are strength and heat resistance. NASA says that you must have a bolt that has the strength of at least X and a heat resistance of at least Y.
But when you make a bolt, there is no way you can make a bolt that equals X and Y all the time; there are just two many factors that go on in the manufacture of a bolt. So what you are looking for are bolts that are at least X or better and at least Y or better. Hence, an inequality. You can only use bolts that are in the correct range for X AND the correct range for Y.
But, of course, to test the bolts, you have to expose them to the extremes of both to see how they measure up. So how can you prove to NASA that your bolts will stand up? As an added problem, you never want to use bolts that you tested because that testing may have made them weaker in the process.
There is an area of Math that is used in the business world all the time to answer this type of question? Does anyone know what this area is called?
The branch of math that you are looking for is called "optimization." Specifically, this type of problem would fall into the category of "linear programming." You are attempting to optimize the quality of the bolts but you have specific ...
A linear programming example is given and discussed.