1. In real world optimisation problems there is often an accompanying constraint that must also be satisfied. These problems are typically solved using "Lagrange Multipliers", which make use of several ideas that you have learned in MAB122.
(a) Consult the library or Internet to investigate how constrained optimisation using Lagrange Multipliers works. Summarise what you find (no more than 1 page).
(b) Use Lagrange Multipliers to determine the point(s) on the surface xy - z^{2} = 1 which are closest to the origin.