In a few weeks, I'll be teaching solving systems of inequalities and one of the first questions a student will ask is "How is this used in real life?" I always struggle to answer this one because I got my degree in theoretical math so I'm great with the math but not so good with the practical.
This is used to determine a solution to situations such as figuring out the number of a product that should be produced to create the most profit or determining the correct mix of drugs for a patient. Imagine its used in medicine.
Its also referred to as the Theorem of Feasible Regions. In other words, it is the set of coordinate pairs that solve a systems of inequalities. Its the region which satisfies restrictions placed in linear programming.
So then what does an inequality represent in real life. In real life, an inequality is recognized by the use of limits such as a speed limit of 75 mph, a minimum payment on your credit card, limit of text messages, or time needed to travel. For any of these examples they are actually inequalities.
The speed limit example means you are not to travel above 75 mph but you could easily travel below it. When you receive the credit card bill, they say you can pay $50 but you can pay more. This is only a minimal suggestion so your payment is $50 or more. Many people choose a plan that says they cannot send more than 250 messages in a month or often we calculate our trip to or from someplace based on time. If everything is right, it takes me a minimum of 5 minutes to walk to work but if the weather is bad, it could take 10 to 15 minutes.
In addition truckers face inequalities all the time when they cross bridges and have to keep track of their weight. An example might be a bridge can only handle trucks whose weight is not over 65,000 pounds. A trucker has to know the weight of his truck and trailer so he knows if he can use the bridge or must plan an alternate route.
Back to driving but not the speed. Another inequality has to do with obtaining your drivers license because in most states you must be 16 in order to get one. This would be a x is greater than or equal to situation but you might have to be 18 to get an unrestricted license. Along these same lines, there are minimal ages for buying liquor or cigarettes. Both of these are inequalities.
There are also thermostats in the cars that operate on inequalities also with voltage regulators and even Body Mass Index.
Its easy to find single examples of inequalities but not for systems of inequalities unless you look into linear algebra or linear programming. At least I have a better idea of how to explain the use of systems of inequalities. I hope you learned some things because I know I did.