“How can we maximize or minimize a set of linear equations?”
Often times, when working on problems, we have multiple variables related by multiple equations. For example, let’s start out with this situation. Let’s say we have two machine parts x and y that cost 2 dollars and 5 dollars to make respectively, symbolically p(x,y) = 2x + 5y. And let’s also say that we have to make a total of 100 machine parts respectively, or x + y = 100 (blue). And let’s also say that 202 times the number of part x and 5 times the number of part y must be equal to 1400, or 20x + 5y = 1400 (green). So how can we find the minimum price that meets all of our production needs? Well, let’s plot it on a graph (pictured), check all of the points of intersection (In this case (0,100), (60,40) and (100,0) ), and then see which of these points return the minimum desired quantity (In this case (0,100) –> $200). Linear programming can be applied to all forms of applications, ranging from engineering economic systems to control theory and even to general business!