This lecture covers optimization concepts including unconstrained optimization, constrained optimization, and linear programming. It provides examples of using linear programming to find the lowest cost production combination and calculating shadow prices. Specifically, it shows finding the lowest £1233 cost combination of 5/3 cases of A and 2/3 cases of B. It also shows using a system of equations to solve for shadow prices of £116.66 per additional labor unit and £3.33 per additional material unit.