inequalities

Question

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.

Does that example make sense to everyone so far?

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?

Answer 1

I'm not sure exactly what the question is looking for, but I'll give this a shot:

 

The problem is not at all one commonly dealt with in "the business world", it's more of an engineering concern.  I am not an engineer, but I have had some time in the business world.  In business it can often be necessary to calculate limits involving multiple variable, much like the engineering problem above.  For those types of problems, we use differential equations.  The problem would likely involve what is referred to as a complex differential equation or a partial differential equation, as opposed to the ordinary differential equations we tend to use in business, so (if I am understanding the question) I'm thinking the common area between the problem and the business reference in the question would be:

 

Differential Equations  ??

 

I'm not totally confident in this.  So, Shawna, if this notifies you, since it's been over 4 months from the time you posted this maybe you can enlighten me (having completed your course and possibly been enlightened on these things at this point).