Constraint Minimization - Pen and Paper calculation

Objective: Let `f(x,y)=5-(x-2)^2-2(y-1)^2` `g(x,y)=x+4y-3=0` (1) We solve, `∇f=λ ∇g` To simplify, we introduce ‘Lagrangian function’, L and calculate its critical points `L=f-λg` `∴L=5-(x-2)^2-2(y-1)^2+λ(x+4y-3)` …