MIT mathematician Peter Shor opens this lecture from 18.200 Principles of Discrete Applied Mathematics by defining what a linear program is, then works through two concrete examples: the classic diet problem, where you minimize cost subject to nutritional constraints, and a bake sale problem involving limited ingredients and time. He shows how to convert a linear program into standard form and canonical form, explaining why having consistent formats matters for solving and comparing problems. The lecture closes with an introduction to duality, the idea that every linear program has a paired dual problem whose solution bounds or matches the original. Shor writes on the board throughout, building each formulation step by step rather than presenting finished results, making this a working introduction to optimization theory rather than a survey.