Constraint Minimization calculaion --manually

Objective: f(x,y)=5-(x-2)^2 -2(y-1)^2 By using lagrange multiplier L=5-(x-2)^2 -2(y-1)^2 -lamda(x+4y-3)-----1 by doing partial derivative of x and y L(x)=-2(x-2)-lamda->x=(4-lamda)/2-----2 l(y)=-4(y-1)-4lamda->y=1-lamda--------3 sub x and y in constraint to get lamda (4-lamda)/2+4(1-lamda)=3->lamda=2/3 now sub lamda in eq…