What linear programming optimizes

Linear programming is a field that invents clever algorithms for optimization. Whenever flight schedules, warehouse inventory, or which crops to plant are chosen to get the best possible outcome, that is a linear programming problem, whether or not anyone calls it that.

The running example is a factory that makes cookie mix and donut mix. Each kilogram of cookie mix earns $3$ of revenue and each kilogram of donut mix earns $2$. If $c$ is the kilograms of cookie mix and $d$ is the kilograms of donut mix, then revenue is the objective function $3c + 2d$, and the goal is to make it as large as possible.

The tempting shortcut is to just make enormous amounts of both mixes. That does not work, because production uses up limited resources such as flour, so you cannot make as much as you want. The whole difficulty, and the reason a clever algorithm is worth having, is maximizing that revenue while respecting the limits on what you can actually make.