Why sets of system inequality?

Answer 1

These type of problems can be helpful in decision making, for example you have a limited number of resources (such as a certain amount of land to farm), then you can create inequalities that describe costs and benefits to plant certain types of crops. An area which represents the possible solutions of cost and benefit will be bounded by the inequality lines.

I helped my daughter with an algebra word-problem similar to this (I wish I had it handy). A horse breeder who had a choice between raising quarter-horses or thoroughbreds. Each type of horse would need a certain amount of pasture, and each type would bring in a different amount of money when sold. There were a couple of other constraints, which when graphed, created a bounded area on a cost/benefit graph. The goal of the problem was to find out the optimum number of each type of horse to raise, in order to maximize profits.